Concept explainers
A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of vi = 18.0 m/s. The cliff is h = 50.0 m above a body of water as shown in Figure P4.13. (a) What are the coordinates of the initial position of the stone? (b) What are the components of the initial velocity of the stone? (c) What is the appropriate analysis model for the vertical motion of the stone? (d) What is the appropriate analysis model for the horizontal motion of the stone? (e) Write symbolic equations for the x and y components of the velocity of the stone as a function of time. (f) Write symbolic equations for the position of the stone as a function of time. (g) How long after being released does the stone strike the water below the cliff? (h) With what speed and angle of impact does the stone land?
Figure P4.13
(a)
The coordinates of the initial position of the stone.
Answer to Problem 4.29P
The coordinates of the initial position of the stone is
Explanation of Solution
The speed of stone is
Write the expression for the initial x coordinate of stone
Here,
Write the expression for the initial y coordinate at the top of the cliff
Here,
Conclusion:
Therefore, the coordinates of the initial position of the stone is
(b)
The components of the initial velocity of the stone.
Answer to Problem 4.29P
The components of the initial velocity of the stone are
Explanation of Solution
Write the expression for the initial velocity of stone in x direction
Here,
Write the expression for the initial velocity of stone in y direction
Here,
Conclusion:
Therefore, the initial components of the velocity of the stone are
(c)
A model that explains the vertical motion of the stone.
Answer to Problem 4.29P
In the
Explanation of Solution
The vertical motion of the stone is governed by a free fall motion under constant acceleration
Thus, the motion in the
Conclusion:
Therefore, in the y direction the acceleration is constant.
(d)
A model that explains the horizontal motion of the stone.
Answer to Problem 4.29P
In the x direction the velocity is constant.
Explanation of Solution
In the
Thus, the motion in the
Conclusion:
Therefore, in the x direction, motion is due to constant velocity motion.
(e)
The symbolic equation for the x and y component of the velocity as a function of time.
Answer to Problem 4.29P
The x and y component of the velocity are
Explanation of Solution
In the
The final velocity of stone in x direction is same as the initial velocity in the
Write the relation between the final and initial velocity in the x-direction,
Here,
The velocity in x direction does not depend on time.
In the
Write the expression for final velocity in the y-direction
Here,
Conclusion:
Substitute
Therefore, the x and y component of the velocity are
(f)
The symbolic equation for the x and y component for the position as a function of time.
Answer to Problem 4.29P
The x and y component of the position are
Explanation of Solution
Write the expression for the position of stone in x direction
Here,
Write the expression for the position of stone in y direction
Here,
Conclusion:
Substitute
Substitute
Therefore, the x and y component of the position are
(g)
The time for the stone to strike the water below the cliff.
Answer to Problem 4.29P
The time for the stone to strike the water below the cliff is
Explanation of Solution
Write the formula to calculate time
Conclusion:
Substitute
Therefore, the time for the stone to strike the water below the cliff is
(h)
The speed and angle with which the stone land.
Answer to Problem 4.29P
The speed of the stone is
Explanation of Solution
Write the expression to calculate velocity,
Substitute
Write the formula to calculate speed of stone land
Here,
Write the expression to calculate angle of stone land
Conclusion:
Substitute
Therefore, the speed of the stone at the time of land is
Substitute
Therefore, the angle of the stone land is
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Chapter 4 Solutions
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