Question

A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. the angle of depression of the boat changes from 60° to 45° in 2 minutes. find the speed of the boat in m/h.

Answer 1

find the distance of boat from cliff when angle of elevation is 60° by taking tan60 = height of cliff /distance between boat and cliff it is found that it is
$50 \sqrt{3}$

now in the same way taking angle of elevation as 45°find distance of boat when it is 45 °from the cliff. on finding distance = 150 m
now find the distances between two position of boats
which is
$150 - 50 \sqrt{3}$
= 50(3 -1.732) = 63.4
the boat travels 63.4 m in 2 min or 120 sec
:. speed of boat = distance / time itis wanted m/hr
:. answer should be multiplied by 3600
=63.4×3600/120 =1902 m/hr

Answer 2

therefore the answer is 1902 M per hour