The total time it takes the sound to reach our on top of the cliff (10.0 s) is actually sum of two times:
- the time it takes the rock to hit the ground starting from the top of the cliff, t1
- the time it takes the sound to reach the top of the cliff starting from the ground, t2
1) The rock moves by uniformly accelerated motion, with constant acceleration

. Its law of motion is given by

, where

is the initial velocity of the rock, and h is the height of the cliff. The time t1 is the time at which the rock reaches the ground, so that y(t1)=0, and the equation becomes

2) The sound moves from the ground to the top of the cliff by uniform motion, with constant speed v=343 m/s. Therefore, the sound covers the distance h (the height of the cliff) in a time t2 given by

3) If we rewrite h in both equations, we can write:

(1)
4) We also know that the sum of t1 and t2 is equal to 10 seconds:

from which we find

if we substitute this into eq.(1), we get

Numerically:

Solving the equation, we find the solution

(the other solution is negative, so it does not have physical meaning). As a consequence,

and the height of the cliff is given by
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