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Question

A spotlight is placed at a distance of 4 m from a vertical wall and is rotating at a rate of 1 rad s1. 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
4 ms1
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B
6 ms1
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C
8 ms1
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D
None of these
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Solution

The correct option is C 8 ms1
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=1 rad/s
v=4sec245×1 (when θ=45,ϕ=45)
v=8 ms1

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