Question

A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30º, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60º. Find the time taken by the car to reach the foot of the tower from this point.

Answer 1

Let OA be the tower of height h, and P be the initial position of the car when the angle of depression is 30º.

After 6 seconds, the car reaches to Q such that the angle of depression at Q is 60º. Let the speed of the car be v, meter per second. Then,

PQ=6v (Distance = speed x time)

and let the car take t seconds to reach the tower OA from Q (Fig. 11.39). Then, OQ =vt meters.