The stone falls into the gorge. After 6 seconds, the sound of a stone hitting the ground is heard.

The stone falls into the gorge. After 6 seconds, the sound of a stone hitting the ground is heard. Determine the depth of the gorge. If the speed of sound in air is 330 meters per second.

Distance traveled by a stone when falling into a gorge:

S = g * (t1) ² / 2 = 4.9 * (t1) ², where t1 is the free fall time of a stone in the gorge.

The sound after hitting a stone on the ground traveled a distance equal to the height of the gorge:

S = v * t2 = 330 * t2, where t2 is the time it takes for the sound of a stone hitting the ground to reach the listener’s ears.

So 4.9 * (t1) ² = 330 * t2. (one)

According to the condition, the blow was heard 6 seconds after the fall of the stone, i.e .:

t1 + t2 = 6. (2).

Received the system of equations (1) and (2). Having solved it, we find that:

t1 = 5.54 s, t2 = 0.46 s.

The depth of the gorge:

S = 4.9 * (t1) ² = 4.9 * 5.54² = 150.39 m.