A stone falls from a steep cliff, and after 6 seconds you can hear its knock on the ground.

A stone falls from a steep cliff, and after 6 seconds you can hear its knock on the ground. Determine the height of the rock if the speed of sound in air is 330 m / s

t = 6 s.

g = 10 m / s2.

Vsv = 330 m / s.

h -?

Time t will be the sum: t = tp + tsv, where ts is the time the stone falls from the cliff, tsv is the time it takes for the sound to reach the top of the cliff from the place of impact.

The time of falling of the stone tp is expressed by the formula: tp = √ (2 * h / g), where h is the height of the rock, g is the acceleration of gravity.

The time of sound movement tsv is expressed by the formula: tsv = h / Vsv, where Vsv is the speed of sound propagation.

t = √ (2 * h / g) + h / Vsv.

√h = x.

t = x * √2 / √g + x ^ 2 / Vsv.

x ^ 2 + x * Vsv * √2 / √g – Vsv * t = 0.

x ^ 2 + x * 147.6 – 1980 = 0.

D = (147.6) 2 – 4 * (-1980) = 29706.

x1.2 = (-147.6 ± 172.3) / 2.

x1 = (-147.6 + 172.3) / 2 = 12.35.

√h = 12.35.

h = (12.35) ^ 2 = 152.5 m.

Answer: the rock has a height of h = 152.5 m.