A spotlight is fixed 4 m from the vertical wall and is rotating at a rate 1 rads−1. The spot moves vertically on the wall. Find the speed ( in ms−1) 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=8ms−1