The plane must fly at an angle of 11.31 degrees west of due north to arrive at the destination in the shortest time possible.
To determine the direction that the plane must fly relative to north, we need to first determine the actual velocity of the plane relative to the ground.
Let's break down the velocity vectors involved in the flight:
The air speed of the plane is 120 m/s in a direction perpendicular to the plane's heading (i.e., to the east).
The wind speed is 24 m/s due west.
Using vector addition, we can find the resultant velocity vector of the plane relative to the ground:
The eastward component of the plane's velocity is 120 m/s.
The westward component of the wind's velocity is 24 m/s.
The northward component of the plane's velocity is unknown and will depend on the plane's heading.
We can use the Pythagorean theorem to find the magnitude of the resultant velocity vector:
[tex]resultant speed^2 = eastward speed^2 + northward speed^2[/tex]
[tex]resultant speed^2 = (120 m/s)^2 + northward speed^2[/tex]
resultant speed = [tex]\sqrt{[(120 m/s)^2 + northward speed^2]}[/tex]
Since the destination is directly north of the origin, the plane's heading must be northward. Therefore, the angle between the plane's velocity vector and the northward direction must be the direction we're looking for.
To find this angle, we can use trigonometry. Let theta be the angle between the plane's velocity vector and the northward direction. Then:
tan(theta) = northward speed / 120 m/s
northward speed = 120 m/s * tan(theta)
Substituting this into the equation for the magnitude of the resultant velocity vector, we get:
resultant speed = [tex]\sqrt{[(120 m/s)^2 + (120 m/s * tan(theta))^2]}[/tex]
We want the resultant velocity vector to be equal to the distance between the two points on the ground (500 km) divided by the time of the flight. We can convert this to meters per second by dividing by the duration of the flight in seconds:
resultant speed = 500000 m / (flight time in seconds)
Equating this with the expression we derived for the magnitude of the resultant velocity vector, we get:
500000 m / (flight time in seconds) = [tex]\sqrt{[(120 m/s)^2 + (120 m/s * tan(theta))^2]}[/tex]
Solving for the flight time in seconds and simplifying, we get:
flight time = [tex]500000 m \sqrt{[(120 m/s)^2 + (120 m/s * tan(theta))^2]}[/tex]
To minimize the flight time, we need to maximize the northward component of the plane's velocity. We can do this by making the angle theta as small as possible, i.e., by flying as close to due north as possible.
Taking the derivative of the flight time expression with respect to theta, we get:
d(flight time) / d(theta) =[tex]-60000 * tan(theta) / (120^2 * (1 + tan(theta)^2)^(3/2))[/tex]
Setting this equal to zero, we find that the optimal value of theta is arctan(1/5), which is approximately 11.31 degrees. Therefore, the plane must fly at an angle of 11.31 degrees west of due north to arrive at the destination in the shortest time possible.
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An ice skater initially skating at a velocity of 3 m/s speeds up to a velocity of 5 m/s. The momentum of the skater.
"An ice skater initially skating at a velocity of 3 m/s speeds up to a velocity of 5 m/s. The momentum of the skater increases." Correct option is B.
Momentum is given by the equation,
P = mv
where,
m is mass
v is velocity
As mass is maintained constant, the momentum from the given equation is directly proportional to the velocity of the ice skater.
If the velocity of the ice skater increases, then the momentum of the ice skater also increases.
In this problem, the velocity of the ice skater which was initially 3 m/s increases to 5 m/s.
This means that the momentum of the ice skater also increases.
Thus, the momentum tends to increase as velocity increases. The correct option is B.
The given question is incomplete. The complete question is 'A. Remains the same B. Increases C. Becomes zero D. Decreases'
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Estimate the mass of the milky way galaxy from the fact that the sun orbits the galactic center every 230 million years at a distance of 27,000 light-years. (as we'll discuss in chapter 19, this calculation actually tells us only the mass of the galaxy within the sun's orbit. ).
Answer: The estimated mass of the Milky Way galaxy is approximately 1.8 x 10^42 kg.
Explanation:
We can use the orbital velocity of the Sun around the galactic center, the distance from the Sun to the galactic center, and the laws of gravity to estimate the mass of the Milky Way galaxy.
The Sun orbits the galactic center at a velocity of approximately 220 km/s or 486,000 miles per hour. The distance from the Sun to the galactic center is approximately 27,000 light-years, or 1.6 x 10^17 miles.
We can use Kepler's Third Law, which relates an object's orbital period and distance to the mass of the central body, to calculate the galaxy's mass. This law can be written as:
[tex]T^2 = \frac{4\pi ^2}{GM} r^3[/tex]
where T is the orbital period (230 million years),
G is the gravitational constant,
M is the mass of the galaxy,
and r is the distance from the Sun to the galactic center.
Solving for M, we get:
[tex]M = \frac{(\frac{4\pi ^2}{G})r^3}{T^2}[/tex]
Plugging in the values, we get:
[tex]M = \frac{(4\pi ^2 / 6.6743 x 10^-11 m^3/kg/s^2) (1.6 x 10^17 miles)^3}{(230 million years)^2}[/tex]
Converting the units, we get:
M = 1.8 x 10^42 kg
Therefore, the estimated mass of the Milky Way galaxy is approximately 1.8 x 10^42 kg.
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Because weight is a measurement of the amount of gravity pulling on an object, weight is considered a ______.
Answer:
Weight is considered a force, since it is a measurement of the amount of gravity pulling on an object.
What other transformation is used to create this pattern
The other transformation used in creating this pattern other than translation is 180° rotation.
What is pattern transformation?Pattern transformation refers to the process of altering or manipulating a basic pattern in order to create a new and unique design. This can involve changing the scale, orientation, color, or other characteristics of the original pattern.
One common method of pattern transformation is through repetition, where a pattern is repeated in a regular or irregular arrangement. This can create a sense of movement, rhythm, or complexity within the design.
The pattern in the image contains translation and rotation (180°) symmetries, the pattern is referred to as SPINNING HOP according to Conway.
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which one of the following parameters is not used to determine the magnetic force on a current-carrying wire in a magnetic field?
Radius of wire is not used to determine the magnetic force on a current-carrying wire in a magnetic field
What is a magnetic field?A magnetic field is a region in space where magnetic forces can be detected. It is created by the motion of electric charges, such as the movement of electrons in an electric current or the spinning of electrons in an atom.
A magnetic field is represented by lines of force that can be visualized using magnetic field lines. These lines indicate the direction of the magnetic field at each point in space and the strength of the magnetic field is indicated by the density of the lines.
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A ball moving at 11 m/s makes an off-center
elastic collision with another ball of equal
mass that is initially at rest. The incom-
ing ball is deflected at an angle of 29◦ from its
original direction of motion.
Find the speed of the first ball after the
collision.
Answer in units of m/s. Answer in units of
m/s
Answer:
8.65 m/s.
Explanation:
Let's use conservation of momentum and conservation of kinetic energy to solve this problem.
Since the two balls have equal masses, we can simplify the problem by assuming they are identical. Let's call the initial speed of the incoming ball v and the final speed of the outgoing ball v'.
Conservation of momentum tells us that the total momentum before the collision is equal to the total momentum after the collision:
mv = mv'cos(29°) + mv'sin(29°)
where m is the mass of each ball.
Conservation of kinetic energy tells us that the total kinetic energy before the collision is equal to the total kinetic energy after the collision:
(1/2)mv^2 = (1/2)mv'^2
We can solve the first equation for v' and substitute it into the second equation:
v' = v(1 - sin(29°)) / cos(29°)
(1/2)mv^2 = (1/2)m[v(1 - sin(29°)) / cos(29°)]^2
Solving for v', we get:
v' = v[1 - sin(29°)] / cos(29°)
v' = 8.65 m/s (to two decimal places)
Therefore, the speed of the first ball after the collision is 8.65 m/s.
which of the following statements are true? check all that apply. which of the following statements are true?check all that apply. the first law of thermodynamics extends the principle of conservation of momentum to include molecular collisions. the work done by a thermodynamic system depends only on the initial and final states of the system. the amount of heat added or removed from a thermodynamic system depends on the path taken on a pv diagram. the first law of thermodynamics extends the principle of conservation of energy to include heat as well as mechanical energy. the amount of heat added or removed from a thermodynamic system depends only on the initial and final states of the system. the work done by a thermodynamic system is equal to the area under the curve on a pv diagram.
The following statements are true: The first law of thermodynamics extends the principle of conservation of energy to include heat as well as mechanical energy.
The work done by a thermodynamic system is equal to the area under the curve on a pv diagram.
The amount of heat added or removed from a thermodynamic system depends only on the initial and final states of the system.
What is thermodynamics?Thermodynamics is a branch of physics that deals with the relationships between heat, energy, and work. It focuses on the behavior of systems of matter and energy and their interactions with each other. It is widely used in fields such as chemistry, engineering, and materials science to understand and predict the behavior of complex systems.
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What type of transformation has triangle ABC undergone to form the triangle A B C
The type of transformation which triangle ABC has undergone to form the triangle A B C is a vertical reflection which is therefore denoted as option D.
What is Vertical reflection?A vertical reflection reflects a graph vertically across the x-axis, while on the other hand a horizontal reflection reflects a graph horizontally across the y-axis.
The type of transformation on triangle is across the x-axis which us therefore the reason why vertical reflection was chosen as the correct choice.
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Answer:
D. vertical reflection
Explanation:
What is the relationship between a substance’s thermal energy and its kinetic energy? There is no relationship between a substance’s thermal energy and kinetic energy.
There is no relationship between a substance’s thermal energy and kinetic energy.
As the substance’s thermal energy increases, the kinetic energy of its particles increases, and vice versa.
As the substance’s thermal energy increases, the kinetic energy of its particles increases, and vice versa.
As the substance’s thermal energy increases, the kinetic energy of its particles decreases, and vice versa.
As the substance’s thermal energy increases, the kinetic energy of its particles decreases, and vice versa.
A substance’s thermal energy is the same as its kinetic energy.
As the substance's thermal energy increases, the kinetic energy of its particles increases, and vice versa.
What is kinetic energy?The kinetic energy of an object increases as its mass or velocity increases. For example, a heavy object moving at a high speed has more kinetic energy than a lighter object moving at a lower speed. Additionally, the direction of an object's motion is not relevant to its kinetic energy, as long as it is moving. Kinetic energy is a scalar quantity, meaning that it has only magnitude and no direction. It is also a form of mechanical energy, which is energy that is associated with the motion or position of an object. Other forms of mechanical energy include potential energy, which is energy that an object possesses due to its position or configuration, and thermal energy, which is the energy associated with the motion of particles within a substance.
Here,
Thermal energy is a form of energy associated with the motion of particles in a substance. Specifically, thermal energy is the sum of the kinetic energies of the particles in a substance. So, as the temperature of a substance increases, the average kinetic energy of its particles also increases. This means that the particles move faster and have greater kinetic energy. Therefore, there is a direct relationship between a substance's thermal energy and its kinetic energy. If the substance's thermal energy increases, its particles will have more kinetic energy and will move faster. Conversely, if the substance's thermal energy decreases, its particles will have less kinetic energy and will move more slowly.
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Answers:
Question 1: As the substance’s thermal energy increases, the kinetic energy of its particles increases, and vice versa.
Question 2: Its molecules move around more quickly, so there is more space between them, making it less dense than the air above it.
Question 3: Warmer sauce at the bottom of the pot is less dense, so it rises, forcing cooler sauce down, where it is warmed.
Question 4: Hot soup warms the bowl where it sits.
Question 5: transfer of thermal energy through infrared waves
Explanation:
i just did the quick check
for our first example of motion in a plane, suppose you are operating a radio-controlled model car on a vacant tennis court. the surface of the court represents the x -y plane, and you place the origin at your own location. at time t1
(a) The components of the average velocity of the car us 3.64 m/s and (b) The magnitude and direction of the average velocity is 4.54 m/s.
What is average velocity?A vector measure of average velocity exists. In order to calculate average velocity, divide the change in position or displacement (x) by the time intervals (t) during which the displacement takes place. Depending on the displacement's sign, the average velocity can either be positive or negative. The SI unit for average speed is metres per second (m/s or ms-1).
[tex]$$Given that:\\The coordinates of the car $(4.0 \mathrm{~m}, 2.0 \mathrm{~m})$ at $\mathrm{t}_1=2.0 \mathrm{~s}$ \\The coordinates of the car $(7.0 \mathrm{~m}, 6.0 \mathrm{~m})$ at $\mathrm{t}_2=3.1 \mathrm{~s}$[/tex]
[tex]$$(a) The component of the average velocity of the car is:x-component:$$\begin{aligned}& \mathrm{v}_{\mathrm{x}}=\frac{\mathrm{x}_2-\mathrm{x}_1}{\mathrm{t}_2-\mathrm{t}_1} \\& \mathrm{v}_{\mathrm{x}}=\frac{7-4}{3.1-2} \\& \mathrm{v}_{\mathrm{x}}=2.72 \frac{\mathrm{m}}{\mathrm{s}} \\\end{aligned}[/tex]
[tex]\begin{aligned}\\& \mathrm{y} \text {-component: } \\& \mathrm{v}_{\mathrm{y}}=\frac{\mathrm{y}_2-\mathrm{y}_1}{\mathrm{t}_2-\mathrm{t}_1} \\& \mathrm{v}_{\mathrm{y}}=\frac{6-2}{3.1-2} \\& \mathrm{v}_{\mathrm{y}}=3.63 \frac{\mathrm{m}}{\mathrm{s}}\end{aligned}$$[/tex]
[tex]$$(b) The magnitude and direction of the average velocity is$$\begin{aligned}& |\mathrm{v}|=\sqrt{\mathrm{v}_{\mathrm{x}}^2+\mathrm{v}_{\mathrm{y}}^2} \\& |\mathrm{v}|=\sqrt{2.72^2+3.63^2} \\& |\mathrm{v}|=4.54 \frac{\mathrm{m}}{\mathrm{s}}\end{aligned}$$[/tex]
Thus, The components of the average velocity of the car us 3.64 m/s and The magnitude and direction of the average velocity is 4.54 m/s.
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Complete question:
8. Due to his mental illness, Ben has difficulty holding a job. Ben could be considered abnormal under the definition of abnormality as
O A. a legal concept.
O B. deviation from the ideal.
O C. the inability to function effectively
O D. deviation from the average.
Ben's mental illness could be considered abnormal under the definition of abnormality as the inability to function effectively.
The correct answer is C.
How can the mental illness of Ben be considered under abnormality?
According to the definition of abnormality as the inability to function effectively, Ben's difficulty holding a job due to his mental illness would be considered abnormal.
This definition of abnormality is focused on whether a person's behavior is causing them to be unable to effectively carry out their daily tasks and responsibilities. In this case, Ben's mental illness is interfering with his ability to function in a work environment, which is a sign of abnormality.
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One six-sided die and one sixteen-sided die are rolled. What is the probability of rolling an even number on the six-sided die and rolling a 16 on the other die?.
Answer:
The probability of rolling an even number on the six-sided die and rolling a 16 on the other die is 1/30, since there is a 3/6 probability of rolling an even number on the six-sided die and a 1/16 probability of rolling a 16 on the sixteen-sided die.
Oppositely charged parallel plates are separated by 6.04 mm. A potential difference of 600 V exists between the plates. (a) What is the magnitude of the electric field between the plates? 99337.74N /C (b) What is the magnitude of the force on an electron between the plates? 1.58e-14 N (c) How much work must be done on the electron to move it to the negative plate if it is initially positioned 2.84 mm from the positive plate? 4.49e-13
Answer:
which of these is a meneral?
A merry-go-round rotates at the rate of
0.14 rev/s with an 100 kg man standing at
a point 2.1 m from the axis of rotation.
What is the new angular speed when the
man walks to a point 0 m from the center?
Consider the merry-go-round is a solid 83 kg
cylinder of radius of 2.1 m.
Answer in units of rad/s.
part2: What is the change in kinetic energy due to
this movement?
Answer in units of J.
Part 1: The angular speed increases to a new value is 0rad/s. Part 2: the change in kinetic energy is given by Delta -31205.7J.
What is angular speed?Angular speed is a measure of the angular displacement of a rotating object over a period of time. It is measured in revolutions per minute (RPM) or radians per second (rad/s).
Part 1:
The angular speed of the merry-go-round is determined by the rotational inertia of the cylinder, which is given by [tex]I = 1/2 mr^2,[/tex]
where m is the mass and r is the radius of the cylinder. Since the mass of the cylinder is given,
we can calculate the rotational inertia as [tex]I = 83 kg * (2.1 m)^2 / 2 = 352.41 kg m^2.[/tex]
The angular speed of the merry-go-round is given by w = (Torque) / (Inertia).
Since the torque is due to the man's weight, we can calculate the torque as T = mgd,
where m is the mass of the man, g is the gravitational acceleration and d is the distance from the axis of rotation.
In this case, the torque is given by [tex]T = 100 kg * 9.81 m/s^2 * 2.1 m = 2041.1 Nm.[/tex]
The angular speed of the merry-go-round with the man at a distance of 2.1 m from the axis of rotation is then [tex]w = T / I = 2041.1 Nm / 352.41 kg m^2 = 5.78 rad/s.[/tex]
When the man moves to a point 0 m from the center, the torque is reduced to zero and the angular speed increases to a new value given by [tex]w = T / I = 0 Nm / 352.41 kg m^2 = 0 rad/s.[/tex]
Part 2:
The change in kinetic energy due to the man's movement is given by Delta [tex]KE = KE_{final} - KE_{initial}[/tex],
where KE is the kinetic energy of the merry-go-round.
The kinetic energy is given by KE = 1/2 I [tex]\omega^2[/tex],
where I is the rotational inertia and omega is the angular speed. In this case,
the change in kinetic energy is given by Delta [tex]KE = 1/2 * 352.41 kg m^2 * (0 - 5.78 rad/s)^2 = -31205.7 J.[/tex]
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At t = 2s, a certain particle has a speed of 11 m/s and is moving at an angle of 30° above the +2 axis. At t = 6 s the same particle is moving at 5 m/s straight down at angle of 90°
below the +2 axis. Calculate the magnitude of its average acceleration.
The average acceleration is roughly 2.51 m/s2 in magnitude.
What are velocity and acceleration?The pace at which a displacement varies is known as velocity.. . Velocity is a vector quantity because it comprises both magnitude and direction. Acceleration, which is the rate at which velocity changes, is also a vector quantity.
Using the following formula, we can get the particle's average acceleration:
velocity change x time change equals average acceleration.
initial speed:
The initial velocity consists of two parts: one perpendicular to the +2 axis and one parallel to it. The following is the component along the +2 axis:
v1x = v1 cosθ = 11 cos(30°) ≈ 9.55 m/s
v1y = v1 sinθ = 11 sin(30°) ≈ 5.5 m/s
Final velocity:
v2y = -5 m/s
Therefore, the change in velocity is:
Δv = v2 - v1 = -5 m/s - 11 m/s sin(30°) i - 11 m/s cos(30°) j ≈ -10.05 j m/s
Change in time:
The change in time is:
Δt = 6 s - 2 s = 4 s
Adding everything up, the average acceleration is as follows:
|average acceleration| = |Δv / Δt| = |-10.05 j m/s / 4 s| ≈ 2.51 m/s².
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Please help will give 50 Points and brainly due
Answer:
50 kg
Explanation:
Suppose a kangaroo is sitting still on a stationary log that is floating in a lake. When the kangaroo gets scared, she jumps off the log with a velocity of 15 m/s toward the bank. The log moves with a velocity of 3.8 m/s away from the bank. If the mass of the log is 250 kg, what is the mass of the kangaroo? Before Jump Kangaroo Mass (kg) Log Velocity (m/s) Momentum (kg m/s) Mass (kg) Velocity (m/s) Momentum (kg m/s) After Jump Mass (kg) Velocity (m/s) Momentum (kg m/s) Mass (kg) Velocity (m/s) Momentum (kg m/s)
To find the mass of the kangaroo, we must use the law of conservation of momentum, which states that the total momentum of a system remains constant unless an external force acts on it. Before the jump, the momentum of the kangaroo and the log was zero since they were stationary. After the jump, the momentum of the system is equal to the sum of the momentums of the kangaroo and the log, which is equal to (250 kg)(3.8 m/s) + (m)(15 m/s) = 0. Solving for m, we get m = 50 kg. Therefore, the mass of the kangaroo is 50 kg.
Answer:
You should give him the brainly! You gave me one, now it is his turn. And by the way, thank you for the brainliest early. :D
By the way, the answer is 50kg
Explanation:
A baseball rolls off a 0.70 m high desk and strikes the floor 0.25 m away from the base of the desk. How far was the ball rolling?
Answer:0.66m/s
Explanation:
We can calculate the time it takes for the ball to fall to the floor. y = (1/2) a t^2 t = sqrt { 2y / g } t = sqrt { (2) (0.70 m) / (9.80 m/s^2) } t = 0.378 seconds In a time of 0.378 seconds, the ball traveled a horizontal distance of 0.25 meters. We can find the horizontal speed when the ball was rolling on the desk. v = d / t v = 0.25 m / 0.378 s v = 0.66 m/s The ball was rolling at a speed of 0.66 m/s when it was rolling on the desk.
A car, 1800-kg, going 41.7 m/s rear ends a truck, 5500-kg going 27.8 m/s. What are their velocities after an elastic collision in one dimension?
Refer to the image attached.
at which type of plate boundary will a trench most likely form
A 0.60-kg block initially at rest on a frictionless, horizontal surface is acted upon by a force of 7.0 N for a distance of 2.0 m. How much farther would the force have to act for the block to have 57 J of kinetic energy?
Answer:
Explanation:
o have 57 J of kinetic energy?
We can use the work-energy principle to solve this problem. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. The work done by a constant force on an object is given by the product of the force and the distance over which the force is applied.
Let's first find the initial kinetic energy of the block, which is zero because the block is initially at rest. Then we can find the work done by the force:
W = Fd = (7.0 N)(2.0 m) = 14 J
The work done by the force is 14 J. We want to find the additional distance the force would have to act to give the block a total kinetic energy of 57 J. Let x be the additional distance:
Work done by force over x distance:
W = Fd = (7.0 N)(x) = 7x J
The total work done on the block is the sum of the work done by the force and the change in kinetic energy:
W_total = W + ΔK
where ΔK is the change in kinetic energy.
At the final position, the block has 57 J of kinetic energy, so:
W_total = 57 J
We can now solve for the additional distance x:
W_total = W + ΔK
57 J = 14 J + (1/2)mv_f^2
where v_f is the final velocity of the block.
Since the block starts from rest, the final velocity is given by:
v_f^2 = 2ΔK / m
v_f^2 = 2(57 J) / 0.60 kg = 95 m^2/s^2
v_f = sqrt(95) = 9.746 m/s
Now we can solve for x:
57 J = 14 J + (1/2)(0.60 kg)(9.746 m/s)^2 - (1/2)(0.60 kg)(0 m/s)^2
57 J = 14 J + 27.8 J + 0
57 J - 14 J - 27.8 J = 7x J
15.2 J = 7x J
x = 2.17 m
Therefore, the force would have to act for an additional distance of 2.17 m for the block to have 57 J of kinetic energy.
A basketball player makes 39% of her shots from the free throw line. Suppose that each of her shots can be considered independent and that she throws 3 shots. Let x = the number of shots that he makes. What is the probability that she makes 1 shot?.
The probability that the basketball player makes 1 shot is 0.435 or approximately 43.5%.
This is a binomial distribution problem, where we have a fixed number of trials (3 free throws) and each trial has two possible outcomes (make or miss) with a fixed probability of success (39%).
The probability of making exactly 1 shot can be calculated using the binomial probability formula:
[tex]P(X = k) = (n choose k) * p^k * (1-p)^{(n-k)} ^[/tex]
Where:
n is the number of trials (3)
k is the number of successes (1)
p is the probability of success on each trial (0.39)
Plugging in the values, we get:
[tex]P(X = 1) = (3 choose 1) * 0.39^1 * (1-0.39)^{(3-1)}[/tex]
= [tex]3 * 0.39 * 0.61^2[/tex]
= 0.435
Therefore, the probability that the basketball player makes 1 shot is 0.435 or approximately 43.5%.
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what type of posterior ligament and cruciate ligament ?
Answer:
one of several ligaments that connect the femur (thighbone) to the tibia (shinbone).
Answer: The posterior cruciate ligament (PCL) is the strongest ligament in the knee. It extends from the top-rear surface of the tibia (bone between the knee and ankle) to the bottom-front surface of the femur (bone that extends from the pelvis to the knee).
Find the velocities of iron blocks weighing 50 kg and 100 kg if they are dropped from a height of 100 m at the same time.
Answer:
44.294 m/s
you might want to double check the answer depending on what you use for g. some people use 9.81, some 9.8, and some 10. that can effect the final answer
Explanation:
use the formula [tex]v^{2}-v_{0}^{2} = 2ax[/tex], which can be moved around to get [tex]v = \sqrt{2ax}[/tex]
note that mass does not effect the velocity
since the blocks were dropped from rest, v_0 = 0m/s. a = g = 9.81 m/s^2, and x = h = 100m.
plug in the values for the variables to get v = sqrt(2(9.81)(100)) = 44.294 m/s for both blocks
In a carnival game, the player throws a ball at a haystack. For a typical throw, the ball leaves the hay with a speed exactly one-half of the entry speed.
The required expression for typical entry speed is [tex]u=4.3818\sqrt{\frac{1}{m}}[/tex]. And, the required value for a typical entry speed is 5.24 m/s.
According to the work-energy theorem, The overall work performed on an object is equal to the change in the object's gravitational and kinetic energies. The work performed by the force is equivalent to this change in kinetic energy. The frictional force value is negative.
This is given by [tex]W=f_s s=\frac{1}{2}mv^2-\frac{1}{2}mu^2[/tex]. Here, initial speed and final speed are denoted by u and v, and the frictional force is denoted by [tex]f_s[/tex]. then substitute v = u/2, and we get an expression for entry speed,
[tex]\begin{aligned}W=-f_s s&=\frac{1}{2}m\left(\frac{u}{2}\right)^2-\frac{1}{2}mu^2\\-f_ss&=\frac{1}{2}mu^2\left(\frac{1}{4}-1\right)\\&=\frac{1}{2}mu^2\left(-\frac{3}{4}\right)\\u^2&=\frac{8f_ss}{3m}\\u&=\sqrt{\frac{8f_ss}{3m}}\\u&=\mathrm{\sqrt{\frac{(8)(6.0\;N)(1.2\;m)}{3m}}}\\&=4.3818\sqrt{\frac{1}{m}}\end{aligned}[/tex]
The required answer for part A is [tex]u=4.3818\sqrt{\frac{1}{m}}[/tex].
Then, the typical entry speed of the ball is calculated as follows,
[tex]\begin{aligned}u&=4.3818\sqrt{\frac{1}{m}}\\&=4.3818\sqrt{\frac{1}{0.70}}\\&=\mathrm{5.24\;m/s}\end{aligned}[/tex]
The required answer for part B is 5.24 m/s.
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The complete question is -
In a carnival game, the player throws a ball at a haystack. For a typical throw, the ball leaves the hay with a speed of exactly one-half of the entry speed.
Part A: If the frictional force exerted by the hay is a constant 6.0 N and the haystack is 1.2 m thick, derive an expression for the typical entry speed as a function of the inertia of the ball. Assume horizontal motion only, and ignore any effects due to gravity.
Part B: What is the typical entry speed if the ball has an inertia of a 0.70 kg?
Melody and her mom beth both have similar fitness lifestyles. Both complete body mass index (bmi) measurements, along with skinfold caliper measurements. They are both found to have the same bmi, but beth's skinfold caliper shows a slightly higher amount of total body fat. This is likely because.
They are both found to have the same BMI, but Beth's skinfold caliper shows a slightly higher amount of total body fat. This is likely because She is older. The correct option is B.
What is a good BMI for a woman?For the majority of women, a BMI of 18.5-24.9 is regarded as normal or healthy. Although BMI can be used as a screening tool by healthcare providers, they shouldn't use it to determine a person's body fat percentage or overall health ( 32 ). Do not forget that health is so much more than body weight or composition.
How can I determine my BMI in kilogrammes?BMI is calculated using the metric system, which divides weight in kilogrammes by height in metres squared. As height is often measured in millimetres, a different calculating procedure can be employed. It involves dividing the weight in kilogrammes by the square of the height in centimetres, then multiplying the result by 10,000.
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The complete question is -
Melody and her mom Beth both have similar fitness lifestyles. Both complete body mass index (bmi) measurements, along with skinfold caliper measurements. They are both found to have the same bmi, but beth's skinfold caliper shows a slightly higher amount of total body fat. This is likely because
A-She is more athletic
B-She is older
C-She is taller
D-She measured incorrectly
Identical metal spheres are initially charged as shown. Spheres P and Q are touched together and then separated. Then spheres Q and R are touched together and separated. Afterward, the charge on sphere R is A)-1 nC or less . B)-0.5 nC C) 0 nC D) +0.5 nC E) +1 nC or more +4 nC-2
The potential of the two aluminum spheres will be equal when they come into contact. identical radius, therefore equal potential results in charges. Hence, sphere C will have a final charge of q c = +1.125q.
Why does a sphere not have a charge?All charges in a circular conductor are at suitable intervals from one another because the energy in a sphere conductor will travel about until it is evenly distributed across its surface. As a result, there's an equal and opposite charge for every charge. Electric fields produced by these charges cancel each other out.
In a spherical, how is the charge distributed?This is just Qr40r if the charge is evenly dispersed throughout the sphere. The charge contained inside radius r in this instance is Qr, and if the charge is Q(r3/a3) is uniformly distributed around the sphere. Hence, Qr240a3 represents that portion of the potential.
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Which electromagnet is the strongest?
An illustration of a metal bar with a coil of wire around it.
An illustration of a metal bar with a coil of wire around it it has more coils.
An illustration of a metal bar with a coil of wire around it it has less coils.
* The Answer is the 2nd picture - An illustration of a metal bar with a coil of wire around it it has more coils.
Therefore, of the three options given, the electromagnet with more coils around the metal rod is the most powerful if all other factors such as current and core material are kept constant.
What is the very short response to an electromagnet?
An electromagnet is a temporary magnet made by winding a wire around an iron core. When current flows through the coil, iron becomes a magnet, and when the current is cut off, it loses its magnetic properties.
What is Electromagnetism?
Electromagnetism is the branch of physics that deals with the electromagnetic forces that occur between charged particles. Electromagnetic force is one of the four basic forces and describes the electromagnetic field.
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Answer: The answer is B
Explanation:
How mechanical energy can be transformed into wind energy and how
Explanation:
As wind moves past the blades of a wind turbine, it moves or rotates the blades. These blades turn a generator. A generator works as an inverse of an electric motor; instead of applying electrical energy to turn it and create mechanical energy, it uses mechanical energy to turn and create electrical energy. SIMPLE WORDS: a wind turbine moves which is mechanical energy and the way it moves is by the wind blowing and it goes both ways mechanical energy into wind energy wind energy into mechanical and when turbines move it creates wind also
How many seconds will light leaving New York City take to reach the following locations Los Angeles (about 4500km) Tokyo(about 11,000km) the moon /400,000 km) mars (0.5 a.u from earth at its closest approach)
A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9. 8 m/s2 for g. Use 1000 kg/m3 as the weight density of water. Assume that a = 4 m, b = 4 m, c = 9 m, and d = 4 m. )
The work required to pump the water out of the spout is 11,011,392 J.
What is a spout?
A spout is typically a small opening or nozzle through which a fluid (such as water) can flow. The spout may be a part of a container, such as a tank or a pitcher, or it may be a separate attachment, such as a faucet or a sprinkler. The spout is important in the study of fluid dynamics, which is the branch of physics that deals with the motion of fluids and the forces that act on them.
To find the work required to pump the water out of the spout, we need to determine the weight of the water in the tank and the height through which the water needs to be lifted.
The weight of the water in the tank can be found using its volume and weight density. The volume of the tank is given by:
V = a * b * c = 4 m * 4 m * 9 m = 144 [tex]m^{3}[/tex]
The weight of the water can be found using the:
W = m * g = V * ρ * g
where m is the mass of the water, g is the acceleration due to gravity, and ρ is the weight density of water.
Substituting the given values, we have:
W = V * ρ * g = 144 [tex]m^{3}[/tex] * 1000 kg/[tex]m^{3}[/tex] * 9.8 m/[tex]s^{2}[/tex] = 1,411,200 N
Next, we need to determine the height through which the water needs to be lifted. This is equal to the distance from the spout to the surface of the water in the tank. The height can be found using the Pythagorean theorem since the spout is at a diagonal distance from the base of the tank. The height is given by:
h = sqrt([tex]c^{2}[/tex] - [tex]d^{2}[/tex]) = sqrt(9 [tex]m^{2}[/tex] - 4 [tex]m^{2}[/tex]) = 7.81 m
Finally, the work required to pump the water out of the spout is given by:
W = F * d
where F is the force required to lift the water and d is the distance over which the force is applied. The force required to lift the water is equal to its weight, which we calculated earlier. Therefore, we have:
W = F * d = W * h = 1,411,200 N * 7.81 m = 11,011,392 J
Therefore, The amount of work needed to pump the water out of the spout is 11,011,392 joules.
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