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.
Fig.
It is given that the angle of depression at A and B from the top of a tower be 30° and 60° respectively.
Let the speed of the car be v second per minute. Then
AB = distance travelled by the car in 6 s.
= (6 × v) sec. (Dist = speed × time)
= 6v sec.
Let the car takes t minutes to reach the tower CD from B.
Then,
BC = distance travelled by car in t minutes
= (v × t) metres = vt sec.
In right triangle BCD, we have
In right triangle ACD, we have
Comparing (i) and (ii), we get
Hence, the time taken by the car to reach the foot of the tower is 3 sec.
