Question

A man in a boat being rowed away from a cliff 120(3+1) m high takes two minutes to change the angle of elevation of the top of the cliff from 45 to 30. Find the speed of the boat in km/hr.

Answer 1

Let the hieght of lighthouse be y

distance of boat initially = 150m

distance of boat from one point to another = x

thus

According to question

tan 60 = y / 150

thus     y = 150 root 3

tan 45 = y / x+150

1 = y / x + 150

Thus

y = x + 150

150 root 3 = x + 150

x = 150 (root3 - 1)

thus in 2 min speed will be

u = x/t = 75 (root3 -1)