From the window of a building, a ball is tossed from
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From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 8.10 m/s and angle of 22.0° below the horizontal. It strikes the ground 4.00 s later.
| xi | = |
0
|
| yi | = |
y0
|
(b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity.
| vi, x | = | m/s |
| vi, y | = | m/s |
(c) Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: y0 and t. Assume SI units.)
| x | = |
7.5101t
|
| y | = |
−3.0343t−4.905t2
|
(d) How far horizontally from the base of the building does the ball strike the ground?
m
(e) Find the height from which the ball was thrown.
m
(f) How long does it take the ball to reach a point 10.0 m below the level of launching?
s
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- From the window of a building, a ball is tossed from a height yo above the ground with an initial velocity of 7.90 m/s and angle of 25.0° below the horizontal. It strikes the ground 5.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: Yo. Assume SI units. Do not substitute numerical values; use variables only.) x₁ = 0 Y₁ = (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity. Vi,x= Vi, y = (c) Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: yo and t. Assume SI units.) X = y = X m m/s m/s m m (d) How far horizontally from the base of the building does the ball strike the ground? (e) Find the height from which the ball was thrown. m (f) How long does it take the ball to reach a point 10.0 m below the…From the window of a building, a ball is tossed from a height y, above the ground with an initial velocity of 9.10 m/s and angle of 25.0° below the horizontal. It strikes the ground 6.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: Yo: Assume SI units. Do not substitute numerical values; use variables only.) X; = Y; = (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity. V m/s m/s (c) Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: Yo and t. Assume SI units.) X = m y = m (d) How far horizontally from the base of the building does the ball strike the ground? (e) Find the height from which the ball was thrown. m (f) How long does it take the ball to reach a point 10.0 m below the level of launching? SFrom the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 7.50 m/s and angle of 18.0° below the horizontal. It strikes the ground 5.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0. Assume SI units. Do not substitute numerical values; use variables only.) xi = − yi = (c) Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: y0 and t. Assume SI units.) x = y = (f) How long does it take the ball to reach a point 10.0 m below the level of launching?
- An object has an initial velocity of 29.0 m/s at 95.0° and an acceleration of 1.90 m/s2 at 200.0°. Assume that all angles are measured with respect to the positive x-axis. (a) Write the initial velocity vector and the acceleration vector in unit vector notation. (b) If the object maintains this acceleration for 12.0 seconds, determine the average velocity vector over the time interval. Express your answer in your unit vector notation.A particle initially located at the origin has an acceleration of a = 4.00j m/s? and an initial velocity of v = 9.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). tî + 2 j) m (b) Find the velocity of the particle at any time t. î + tj) m/s (c) Find the coordinates of the particle at t = 6.00 s. y%3D m (d) Find the speed of the particle at t = 6.00 s. m/s Need Help? Read It Watch It P Type here to searchA golf ball is hit upward, with an initial velocity of 47 meters per second, at an angle of 25° with respect to the horizontal. The ball is hit from a height of 8 meters above the ground. The horizontal distance x from the starting point and the height y above the ground of the ball t seconds after it is hit are given by the parametric equations below. x=(v0cosθ)t y=−4.9t^2+(v0sinθ)t+h Here v0 is the initial velocity, θ is the initial angle with respect to the horizontal, and h is the initial height. Use the equations to answer the following questions. (a)How long is the ball in the air before it first touches the ground?Do not round any intermediate computations. Round your answer to the nearest hundredth. _____ seconds (b)What is the horizontal distance the ball travels before it first touches the ground?Round your answer to the nearest whole number. _____ meters
- From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 8.80 m/s and angle of 16.0° below the horizontal. It strikes the ground 4.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0. Assume SI units. Do not substitute numerical values; use variables only.) xi = yi =From the window of a building, a ball is tossed from a height yo above the ground with an initial velocity of 7.50 m/s and angle of 21.0° below the horizontal. It strikes the ground 6.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: yo: Assume SI units. Do not substitute numerical values; use variables only.) X; = Y = (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity. Vi, x Vi, y = m/s %3D %3D m/s (c) Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: yo and t. Assume SI units.)You can use any coordinate system you like in order to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity v at an angle 0 with respect to the horizontal. Let the building be 54.0 m tall, the initial horizontal velocity be 9.10 m/s, and the initial vertical velocity be 10.5 m/s. Choose your coordinates such that the positive y-axis is upward, and the x-axis is to the right, and the origin is at the point where the ball is released. (a) With these choices, find the ball's maximum height above the ground and the time it takes to reach the maximum height. maximum height above ground time to reach maximum height (b) Repeat your calculations choosing the origin at the base of the building. maximum height above ground time to reach maximum height
- In the figure, a ball is thrown leftward from the left edge of the roof, at height h above the ground. The ball hits the ground 1.60 s later, at distance d = 26.0 m from the building and at angle 0 = 67.0° with the horizontal. (a) Find h. (Hint: One way is to reverse the motion, as if on videotape.) What are the (b) magnitude and (c) angle relative to the horizontal of the velocity at which the ball is thrown (positive angle for above horizontal, negative for below)? (a) Number 48.71 (b) Number 27.84 (c) Number i 54.28 Units m Units Units m/s ° (degrees)From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 9.00 m/s and angle of 21.0° below the horizontal. It strikes the ground 4.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0. Assume SI units. Do not substitute numerical values; use variables only.) xi = yi = (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity. vi, x = m/s vi, y = m/s (c) Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: y0 and t. Assume SI units.) x = m y = m (d) How far horizontally from the base of the building does the ball strike the ground? m(e) Find the height from which the ball was thrown. m(f) How…From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 8.60 m/s and angle of 18.0° below the horizontal. It strikes the ground 5.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0.) xi = yi = (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity. vi,x = m/s vi,y = m/s (c) Find the equations for the x- and y- components of the position as functions of time. (Use the following as necessary: y0 and t. Let the variable t be measured in seconds.) x = m y = m (d) How far horizontally from the base of the building does the ball strike the ground? m(e) Find the height from which the ball was thrown. m(f) How long does it take the ball to reach a point 10.0 m…