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.
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
h= vt ….(i)
From (i) and (ii),
3vt = 6v+vt
t = 3
Thus, the time taken to reach the shore is 3 minutes.
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