A spotlight is placed at a distance of 4m from a vertical wall and is rotating at a rate of 1rad s−1. The beam moves on the wall. Find the speed of the beam on the wall when the light makes an angle of 45∘ with the horizontal.
A
4ms−1
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B
6ms−1
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C
8ms−1
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D
None of these
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Solution
The correct option is C8ms−1 s is the light shown in the figure and x is the distance moved by the beam in time t.
From the figure, x4=tanϕ ⇒x=4tanϕ
Speed of the beam is given by v=dxdt=4sec2ϕdϕdt
and given dϕdt=ω=1rad/s ∴v=4sec245∘×1 (when θ=45∘,ϕ=45∘) v=8ms−1