Question

c) Two men 960 m apart stand at the same distance from a vertical hillock.
One of them fires a shot and the other hears the echo 2 seconds after
hearing the direct sound. Find the distance of the men from the hillock
assuming the velocity of sound as 320 m/s.
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Answer 1

Given that,

• Distance between the two men = 800 m

• velocity of sound  = 340 m/s

{Distance between the two men from the hillock is same.}

The time taken (t) for the direct sound to be heard by the other man :

• d / v

•  800/340 seconds

• t = 40/17 seconds

Now, since the other man hears the echo 3s after the direct sound is heard ,

Therefore, total time taken(T) to hear the echo = ( t + 3 ) s

•  40/17 + 3 [ solve it by taking LCM ]

• T = 92/17 seconds

Now,

• T = 92/17 s , d (dist. of the two men from the hillock) = ? , v = 340m/s

Therefore,

Distance of the two men from the hillock( = distance of one man from the hillock) = v*T/2

• (340 × 92/17 × 1/2) m

•  920m [ This is the answer ]

Therefore, the Distance between man from the hillock is 920m.

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