A rock is kicked horizontally at a speed of 15 m/s from the edge of a cliff. The rock strikes the ground 65 m from the foot of the cliff of height H as suggested in the figure, which is not drawn to scale. Neglect air resistance.

-What is the approximate value of H, the height of the cliff?
A)27 m
B)54 m
C)78 m
D)150m
E)300 m

Question

A rock is kicked horizontally at a speed of 15 m/s from the edge of a cliff. The rock strikes the ground 65 m from the foot of the cliff of height H as suggested in the figure, which is not drawn to scale. Neglect air resistance.

-What is the approximate value of H, the height of the cliff?

-What is the approximate value of H, the height of the cliff?
A)27 m 
B)54 m 
C)78 m 
D)150m 
E)300 m

Quizplus · Accepted Answer

We can use the kinematic equation: 
y = yo + voy*t + 1/2*ay*t^2 
where y = -H (since we take upward direction as positive), yo = 0, voy = 0, ay = -9.8 m/s^2 (acceleration due to gravity), and t is the time taken for the rock to hit the ground.

We need to find t. We know that horizontal velocity, vx = 15 m/s (given in the problem). 
We also know that horizontal distance, x = 65 m (given in the problem).

x = vx*t 
=> t = x/vx 
=> t = 4.33 s (approx)

Substituting this in the kinematic equation, we get 
-H = -1/2*9.8*(4.33)^2 
=> H = 78.2 m (approx)

Therefore, the answer is choice C, approximately 78 m.

A Rock Is Kicked Horizontally at a Speed of 15