A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of v0 = 16.5 m/s. The cliff is h = 58.0 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 h above a flat stretch of ground below the clifftop. The +x-axis extends 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 g points straight down. (a) What are the coordinates of the initial position of the stone? x0 = m y0 = m (b) What are the components of the initial velocity? v0x = m/s v0y = m/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 t be measured in seconds. Do not include units in your answer.) vx = 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 θ = ° below the horizonta

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter3: Vectors

Section: Chapter Questions

Problem 58PQ: Peter throws a baseball through a houses window. He stands 3.4 m from the window. The ball starts in...

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A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of

v₀ = 16.5 m/s.

The cliff is h = 58.0 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 h above a flat stretch of ground below the clifftop. The +x-axis extends 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 g points straight down.

(a) What are the coordinates of the initial position of the stone?

x₀	=	m
y₀	=	m

(b) What are the components of the initial velocity?

v_0x	=	m/s
v_0y	=	m/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 t be measured in seconds. Do not include units in your answer.)

v_x	=
v_y	=

(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?

v_f	=	m/s
θ	=	° below the horizonta

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