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Question

A spotlight is fixed 4 m from the vertical wall and is rotating at a rate 1 rads1. The spot moves vertically on the wall. Find the speed ( in ms1) of the spot on the wall when the spotlight makes an angle of 45 with the wall.

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Solution

s is the spot light shown in Fig, and x is the distance moved by spot in time t.

From Fig
x4=tanϕ
x=4tanϕ
v=dxdt=4sec2ϕdϕdt
Given dϕdt=ω=1
v=8 ms1

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