Question 101

# A Boat is being rowed away in still water, from a 210 metres high cliff at the speed of 3 km/hr. What is the approximate time taken for the angle of depression of the cliff at the boat to change from 60 deg. To 45 deg.?

Solution

The distance of boat from bottom of cliff when angle of depression is 60 deg is

tan $$60^{\circ}$$ = $$\frac{210}{d}$$

d = 121.3 m

The distance of boat from bottom of cliff when angle of depression is 45 deg is

tan $$45^{\circ}$$ = $$\frac{210}{d}$$

d = 210 m

The distance covered by boat is 210 - 121.3 = 88.7 m

Speed of boat given is 3 km/hr

In m/s it is 3*5/18 = 5/6 m/s = 0.83 m/s

Time taken to cover 88.7 m is 88.7/0.83 = 106.44 sec $$\cong$$ 2 min