A man standing in front of a mountain beats a drum at regular intervals. The rate of drumming is generally increased and he finds that the echo is not heard distinctly when the rate becomes $$40$$ per minute. He then moves nearer to the mountain by $$90$$ m and finds that echo is again not heard when the drumming rate becomes $$60$$ per minute. The distance between the mountain and the initial position of the man is

Question

Infinity Learn · Accepted Answer

For not hearing the echo the time interval between the beats of drum must be equal to time of echo.⇒$$t1=2dv=6040=32$$    ......(i) and $$t2=2(d$$−$$90)v=6060=1$$⇒$$2d$$−$$180=v$$    ......(ii)Form$$ $$(i), we get $$2d=32v$$. Substituting in (ii), we get⇒$$32v$$−$$180=v$$⇒$$180=v2$$⇒$$v=360$$ ms−$$1$$⇒$$2(d)360=32$$⇒$$d=270$$ m.

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