A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of V22.5 m/s. The cliff is h 54.0 m above a flat, horizontal beach as shown in the figure. (a) What are the coordinates of the initial position of the stone? Xo=0 ✔ m X Yo Enter a number. m (b) What are the components of the initial velocity? Vox-22.5 Voy-0 Vy=gt 7 (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.) Vo + ot y= 581² 7 m/s ✔ m/s X (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 ans x= U_t=V_t 0-54.97 x X (e) How long after being released does the stone strike the beach below the cliff? 3.272 ✔S (f) with what speed and angle of impact does the stone land? V-39.2 ✓ 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 V22.5 m/s. The cliff is h 54.0 m above a flat, horizontal beach as shown in the figure. (a) What are the coordinates of the initial position of the stone? Xo=0 ✔ m X Yo Enter a number. m (b) What are the components of the initial velocity? Vox-22.5 Voy-0 Vy=gt 7 (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.) Vo + ot y= 581² 7 m/s ✔ m/s X (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 ans x= U_t=V_t 0-54.97 x X (e) How long after being released does the stone strike the beach below the cliff? 3.272 ✔S (f) with what speed and angle of impact does the stone land? V-39.2 ✓ m/s ✓ below the horizontal
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Can you check section A, C and D

Transcribed Image Text:A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of \( v_0 = 22.5 \, \text{m/s} \). The cliff is \( h = 54.0 \, \text{m} \) above a flat, horizontal beach as shown in the figure.
**Diagram Description:**
- The figure shows a stone being thrown horizontally from the edge of a cliff.
- The stone's path is a curved trajectory downward to the beach.
- Coordinates \( x \) and \( y \) label the horizontal and vertical positions.
**Questions and Solutions:**
**(a) What are the coordinates of the initial position of the stone?**
- \( x_0 = 0 \, \text{m} \)
- \( y_0 = h \, \text{m} \)
**(b) What are the components of the initial velocity?**
- \( v_{0x} = 22.5 \, \text{m/s} \)
- \( v_{0y} = 0 \, \text{m/s} \)
**(c) Write the equations for the \( x \)- and \( y \)-components of the velocity of the stone with time.**
- \( v_x = v_0 + 0t \)
- \( v_y = gt \)
**(d) Write the equations for the position of the stone with time, using the coordinates in the figure.**
- \( x = \frac{U_1 x - V}{T}t \)
- \( y = \frac{1}{2} gt^2 \)
**(e) How long after being released does the stone strike the beach below the cliff?**
- \( 3.272 \, \text{s} \)
**(f) With what speed and angle of impact does the stone land?**
- \( v_f = 39.2 \, \text{m/s} \)
- \( \theta_f = 54.9^\circ \) below the horizontal
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