Question

A rock is dropped from a sea cliff and the sound of it striking the ocean is heard 3.8 s later.

Part A If the speed of sound is 340 m/s, how high is the cliff? Express your answer using two significant figures.

Answer 1

$t_1=\sqrt {\frac {2h}{g}}$ (Time taken by the stone to touch the water.)

$t_2=\frac {h}{v}$ (Time taken by the sound wave to travel the .distance equal to the height of the cliff.)

$t_1+t_2=\frac {h}{v}+\sqrt {\frac {2h}{g}}$

$3.8=\frac {h}{340}+\sqrt {\frac {2h}{9.8}}$

$3.8-2.94h=\sqrt {\frac {2h}{9.8}}$

$9.8\cdot (3.8- 0.0029h)^2=2h$

$9.8\cdot (14.44+0.0000086h^2-0.022h)=2h$

$0.000084h^2-2.215h+141.51=0$

$h=64.04\: m$