A man on a cliff observes a boat at an angle of depression of 30° which is approaching the shore to the point immediately beneath the observer with a uniform speed. Six minutes later, the angle of depression of the boat is found to be 60°. Find the time taken by the boat to reach the shore.

Asked by Topperlearning User | 27th Jul, 2017, 11:02: AM

Expert Answer:

Let A and D be the positions of the boat at the two instants. Let the speed of the boat be v m/min. Therefore, AD= 6v metres Let the boat takes t minutes to reach from D to B. Thus, BD= vt metres In DBC, = tan60o = h= vt ….(i) In ABC, = tan30o = h= ….(ii) From (i) and (ii), vt = 3vt = 6v+vt 2vt=6v t = 3 Thus, the time taken to reach the shore is 3 minutes.

Aswered by  | 27th Jul, 2017, 01:02: PM

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