Question

A rock is dropped from a sea cliff, and the sound of it striking the ocean is heard 3.7 s later.

If the speed of sound is 340 m/s, how high is the cliff?

Answer 1

consider the motion of rock from Top of cliff to ocean or A to B

h = height of cliff = vertical displacement of rock from A to B

t_r = time taken by rock to hit the ocean

a = acceleration due to gravity = 9.8 m/s²

v_i = initial velocity of rock at the top of cliff = 0 m/s

using the equation

h = v_i t_r + (0.5) a t_r²

h = 0 t_r + (0.5) (9.8) t_r²

h = 4.9 t_r²

t_r = sqrt(h/4.9) eq-1

consider the motion of sound the rock hits the ocean from B to A

h = distance travelled by sound

v_s = speed of sound = 340 m/s

t_s = time taken by sound to travel the distance B to A

time taken by sound to travel the distance B to A is given as

t_s = h/v_s

t_s = h/340 eq-2

given that

t_r+ t_s = 3.7

using eq-1 and eq-2

sqrt(h/4.9)  +  h/340 = 3.7

h = 60.75 m