From the window of a building, a ball is tossed from a height yo above the ground with an initial velocity of 7.80 m/s and angle of 21.0° 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 = Y₁ = (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity. V₁ Vi, x V₁, 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 = m/s m/s m m (d) How far horizontally from the base of the building does the ball strike the ground? m m (e) Find the height from which the ball was thrown. (f) How long does it take the ball to reach a point 10.0 m below the level of launching? S
From the window of a building, a ball is tossed from a height yo above the ground with an initial velocity of 7.80 m/s and angle of 21.0° 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 = Y₁ = (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity. V₁ Vi, x V₁, 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 = m/s m/s m m (d) How far horizontally from the base of the building does the ball strike the ground? m m (e) Find the height from which the ball was thrown. (f) How long does it take the ball to reach a point 10.0 m below the level of launching? S
Transcribed Image Text:From the window of a building, a ball is tossed from a height \( y_0 \) above the ground with an initial velocity of 7.80 m/s and angle of 21.0° 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: \( y_0 \). Assume SI units. Do not substitute numerical values; use variables only.)
\[
x_i = \_\_\_
\]
\[
y_i = \_\_\_
\]
**(b)** With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity.
\[
v_{i,x} = \_\_\_ \text{ m/s}
\]
\[
v_{i,y} = \_\_\_ \text{ m/s}
\]
**(c)** Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: \( y_0 \) and \( t \). Assume SI units.)
\[
x = \_\_\_ \text{ m}
\]
\[
y = \_\_\_ \text{ m}
\]
**(d)** How far horizontally from the base of the building does the ball strike the ground?
\[
\_\_\_ \text{ m}
\]
**(e)** Find the height from which the ball was thrown.
\[
\_\_\_ \text{ m}
\]
**(f)** How long does it take the ball to reach a point 10.0 m below the level of launching?
\[
\_\_\_ \text{ s}
\]
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![From the window of a building, a ball is tossed from a height \( y_0 \) above the ground with an initial velocity of 7.80 m/s and angle of 21.0° 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: \( y_0 \). Assume SI units. Do not substitute numerical values; use variables only.)
\[
x_i = \_\_\_
\]
\[
y_i = \_\_\_
\]
**(b)** With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity.
\[
v_{i,x} = \_\_\_ \text{ m/s}
\]
\[
v_{i,y} = \_\_\_ \text{ m/s}
\]
**(c)** Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: \( y_0 \) and \( t \). Assume SI units.)
\[
x = \_\_\_ \text{ m}
\]
\[
y = \_\_\_ \text{ m}
\]
**(d)** How far horizontally from the base of the building does the ball strike the ground?
\[
\_\_\_ \text{ m}
\]
**(e)** Find the height from which the ball was thrown.
\[
\_\_\_ \text{ m}
\]
**(f)** How long does it take the ball to reach a point 10.0 m below the level of launching?
\[
\_\_\_ \text{ s}
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