A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car as an angle of depression of 30°, 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 60°. Find the time taken by the car to reach the foot of the tower from this point.
Let AB be the vertical tower. Suppose D and C be the positions of the car when the angle of depression from the top of the tower is 30° and 60° respectively.
Consider the uniform speed of the car be ν m/sec.
Time taken for the angle of depression to change from 30° to 45° = 10 sec (Given)
∠EAD = ∠ADB = 30° (Alternate angles)
∠EAC = ∠ACB = 60° (Alternate angles)
Suppose AB = h m and BC = x m.
CD = Distance covered by car in 10 sec = ν m/sec × 10 sec = 10 ν m
In triangle ABD
From (1) and (2), we get
now time taken by the car to reach the tower is from C = x / v
therefore time taken by the car to reach the foot of the tower = 5 sec