A person standing in front of a cliff fires a gun and hears its echo after 3s. If the speed of sound in air is $336 \mathrm{~ms}^{-1}$. After moving a certain distance from the cliff, he fires the gun again and this time the echo is heard 1.5 s later than the first. Calculate distance moved by the person.
Explanation
The time taken for the sound to travel from the cliff to the person and back is 3s. The time taken for the sound to travel from the cliff to the person and back after the person moves a certain distance is 4.5s. Let's assume the distance moved by the person is x. The speed of sound is 336 ms^-1. Using the formula time = distance/speed, we can write the equation for the first case as 3 = 2x/336 and for the second case as 4.5 = (2x + 2d)/336, where d is the distance from the cliff to the person. Solving these equations, we get x = 1008 m.
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