Question

A moving boat is observed from the top of a 1550 m high cliff moving away from the cliff. The angle of depression of the boat changes from ${60}^{\circ }$ to ${45}^{\circ }$ in 2 mintues. 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 = $\frac{distance}{time}$

We need to convert it into m/hr
:. answer should be multiplied by 3600
=$63.4\times \frac{3600}{120}$ =1902 m/hr