A straight highway leads to 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.
Let PQ = h metres be the height of the tower. P is the top of the tower.
The first and second positions of the car are at A and B respectively.
APX = 30o PAQ = 30o
BPX = 60o PBQ = 60o
Let the speed of the car be x m/second
Then, distance AB = 6x meters
Let the time taken from B to Q be n seconds
BQ = nx metres
From (1) and (2),
n = 3
Hence, the time taken by the car to reach the foot of the tower from B is 3 seconds.
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