(Q2) A straight highway leads to the foot of a tower. Ramaiah standing at the top of the tower observes a car at an angle of depression 30^o. The car 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^o.Find the time taken by the car to reach the foot of the tower from this point.

Solution :

Let the distance travelled by the car in 6 seconds = AB = x meters

Heights of the tower, CD = h meters

The remaining distance to be travelled by the car BC = d meters

and AC = AB + BC = (x + d) meters

∠PDA = ∠DAB = 30^o

∠PDB = ∠DBC = 60^o

From ∆BCD

h = √ d .....(1)

From ∆ACD

From (1) & (2), we have

x + d = d

x = d

Time taken to travel 'x' meters = 6 seconds.

Time taken to travel the distance of 'd' meters