A person standing in front of a cliff fires a gun and hears its echo after 3s. Speed of sound in air is 336 m s-1.
(a) Calculate the distance of the person from the cliff.
(b) 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 the distance that the person has moved.
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(a) Given,
Time taken to hear the echo = 3s
Speed of sound = 336 ms-1
So,
$$\begin{aligned}\text {Distance of the person from the cliff} = \frac {\text {Speed of sound} \times \text {Time taken}}{2} \\[1 em] =\frac{336 \times 3}{2} = \frac{1008}{2} \\[1 em] = 504\ \text m\end{aligned}$$
So, distance of the person from the cliff is 504 m.
(b) Given,
Time taken to hear the new echo = 3 s + 1.5 s = 4.5 s
So,
$$\begin{aligned}\text {New distance of the person from the cliff} = \frac {\text {Speed of sound} \times \text {Time taken}}{2} \\[1 em] =\frac{336 \times 4.5}{2} = \frac{1512}{2} \\[1 em] = 756\ \text m\end{aligned}$$
Distance moved by the person = 756 - 504 = 252 m
So, distance moved by the person is 252 m.