A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of v0 = 20.5 m/s. The cliff is h = 34.0 m above a flat, horizontal beach as shown in the figure. A student stands on the edge of a cliff with his hand a height habove a flat stretch of ground below the clifftop. The +x-axisextends to the right along the ground and the +y-axis extends up from the ground to the top of the cliff. The origin O of the coordinate plane is directly below the student's hand where the base of the cliff meets the flat ground. The student throws a stone horizontally rightward with initial velocity vector v0.The stone falls with a parabolic trajectory, hitting the ground with a velocity vector v that points down and right. Vector gpoints straight down. (a) What are the coordinates of the initial position of the stone? x0 = 0m y0 = 34m (b) What are the components of the initial velocity? v0x = 20.5m/s v0y = 0m/s (c) Write the equations for the x- and y-components of the velocity of the stone with time. (Use the following as necessary: t. Let the variable tbe measured in seconds. Do not include units in your answer.) vx = 20.5 vy = (d) Write the equations for the position of the stone with time, using the coordinates in the figure. (Use the following as necessary: t. Let the variable t be measured in seconds. Do not state units in your answer.) x = y = (e) How long after being released does the stone strike the beach below the cliff? s (f) With what speed and angle of impact does the stone land? vf = m/s ? = ° below the horizontal
A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of v0 = 20.5 m/s. The cliff is h = 34.0 m above a flat, horizontal beach as shown in the figure. A student stands on the edge of a cliff with his hand a height habove a flat stretch of ground below the clifftop. The +x-axisextends to the right along the ground and the +y-axis extends up from the ground to the top of the cliff. The origin O of the coordinate plane is directly below the student's hand where the base of the cliff meets the flat ground. The student throws a stone horizontally rightward with initial velocity vector v0.The stone falls with a parabolic trajectory, hitting the ground with a velocity vector v that points down and right. Vector gpoints straight down. (a) What are the coordinates of the initial position of the stone? x0 = 0m y0 = 34m (b) What are the components of the initial velocity? v0x = 20.5m/s v0y = 0m/s (c) Write the equations for the x- and y-components of the velocity of the stone with time. (Use the following as necessary: t. Let the variable tbe measured in seconds. Do not include units in your answer.) vx = 20.5 vy = (d) Write the equations for the position of the stone with time, using the coordinates in the figure. (Use the following as necessary: t. Let the variable t be measured in seconds. Do not state units in your answer.) x = y = (e) How long after being released does the stone strike the beach below the cliff? s (f) With what speed and angle of impact does the stone land? vf = m/s ? = ° below the horizontal
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Question
A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of
v0 = 20.5 m/s.
The cliff is h = 34.0 m above a flat, horizontal beach as shown in the figure.
A student stands on the edge of a cliff with his hand a height habove a flat stretch of ground below the clifftop. The +x-axisextends to the right along the ground and the +y-axis extends up from the ground to the top of the cliff. The origin O of the coordinate plane is directly below the student's hand where the base of the cliff meets the flat ground. The student throws a stone horizontally rightward with initial velocity vector v0.The stone falls with a parabolic trajectory, hitting the ground with a velocity vector v that points down and right. Vector gpoints straight down.
(a) What are the coordinates of the initial position of the stone?
(b) What are the components of the initial velocity?
(c) Write the equations for the x- and y-components of the velocity of the stone with time. (Use the following as necessary: t. Let the variable tbe measured in seconds. Do not include units in your answer.)
(d) Write the equations for the position of the stone with time, using the coordinates in the figure. (Use the following as necessary: t. Let the variable t be measured in seconds. Do not state units in your answer.)
(e) How long after being released does the stone strike the beach below the cliff?
s
(f) With what speed and angle of impact does the stone land?
| x0 | = | 0m |
| y0 | = | 34m |
(b) What are the components of the initial velocity?
| v0x | = | 20.5m/s |
| v0y | = | 0m/s |
(c) Write the equations for the x- and y-components of the velocity of the stone with time. (Use the following as necessary: t. Let the variable tbe measured in seconds. Do not include units in your answer.)
| vx | = |
20.5
|
| vy | = |
|
(d) Write the equations for the position of the stone with time, using the coordinates in the figure. (Use the following as necessary: t. Let the variable t be measured in seconds. Do not state units in your answer.)
| x | = |
|
| y | = |
|
(e) How long after being released does the stone strike the beach below the cliff?
s
(f) With what speed and angle of impact does the stone land?
|
vf
|
= | m/s |
| ? | = | ° below the horizontal |
Expert Solution
Step 1
Given:
The height of the cliff is .
The initial velocity of the stone (projectile) is .
The angle of projection is .
The acceleration due to the gravity is .
Diagram:
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