(c) Write the equations for the x- and y-components of the velocity of the pebble with time. (Use the following as necessary: t. Assume that v, and v, are in m/s and t is in seconds. Do not include units in your answers.) V If air resistance can be ignored, what's true about the x-component of the velocity? How does it relate to the initial voy you found in part (b)? m/s V gt oy What is the acceleration? What is its direction? What equation relates the velocity to the initial velocity, acceleration, and time? m/s (d) Write the equations for the position of the pebble with time, using the coordinates in the figure. (Use the following as necessary: t. Assume that x and y are in meters and t is in seconds. Do not include units in your answers.) X+ vot If the velocity is constant in the x-direction, how is the position along the x-axis related to the initial voy and the time? m y = Yo What is the acceleration? What is its direction? What equation relates the y-displacement to the acceleration in the y-direction, the initial velocity in the y-direction, and the time? m (e) How long (in s) after being released does the pebble strike the ground below the cliff? 3.25 (f) With what speed (in m/s) and angle of impact (in degrees clockwise from the +x-axis) does the pebble land? V, = 37.60 e = 64 v m/s What is the final x-component of velocity? The final y-component of velocity? How can you use them and trigonometric functions to determine the angle? Note horizontal (dlockwise from +x) is reuired. ° clockwise from the +x-axis positive angle measured below

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter3: Vectors

Section: Chapter Questions

Problem 3.62AP: After a ball rolls off the edge of a horizontal table at time t = 0, its velocity as a function of...

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A person stands at the edge of a cliff and throws a pebble horizontally over the edge with a speed of v₀ = 20.0 m/s. The pebble leaves his hand at a height of h = 52.0 m above level ground at the bottom of the cliff, as shown in the figure. Note the coordinate system in the figure, where the origin is at the bottom of the cliff, directly below where the pebble leaves the hand.

(c) Write the equations for the x- and y-components of the velocity of the pebble with time. (Use the following as necessary: t. Assume that v, and v, are in m/s and t is in seconds. Do not include units in your
answers.)
V
V, =
If air resistance can be ignored, what's true about the x-component of the velocity? How does it relate to the initial voy you found in part (b)? m/s
V
gt
Vy =
oy
What is the acceleration? What is its direction? What equation relates the velocity to the initial velocity, acceleration, and time? m/s
(d) Write the equations for the position of the pebble with time, using the coordinates in the figure. (Use the following as necessary: t. Assume that x and y are in meters and t is in seconds. Do not include units
in your answers.)
X =
+ vot
If the velocity is constant in the x-direction, how is the position along the x-axis related to the initial voy and the time? m
1
y = Yo
What is the acceleration? What is its direction? What equation relates the y-displacement to the acceleration in the y-direction, the initial velocity in the y-direction, and the time? m
(e) How long (in s) after being released does the pebble strike the ground below the cliff?
3.25
(f) With what speed (in m/s) and angle of impact (in degrees clockwise from the +x-axis) does the pebble land?
37.60
v m/s
64
What is the final x-component of velocity? The final y-component of velocity? How can you use them and trigonometric functions to determine the angle? Note a positive angle measured below
horizontal (clockwise from +x) is required. ° clockwise from the +x-axis

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Given data:

Initial velocity, $v_{0} = 20 m / s$

Height, $h = 52 m$

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