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 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.

Answer 1

Let the height of tower, PQ = h m. 

Px = Horizontal line 

Let the positions of 1^st car and 2^nd car be A and B. 

∠APx = 30° 

∴ ∠PAQ = 30° 

∠BPx = 60° 

∠PBQ = 60° 

Let speed of car be x m/s. 

∴ Distance, AB = 6x m. 

Time required to travel from B to Q be ‘n’ seconds, 

∴ Distance, BQ = nx m