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Question

A spot  light S rotates in a horizontal plane with a constant angular velocity of 0.1 red /s The spot of light ? P move along the wall at a distance 3 m. What of the velocity spot P when  θ = 45o?

Options

A.0.6 m/s
B.0.5 m/s
C.0.4 m/s
D.0.3 m/s

Solution


Let x is the distance of point P from O, the form figure
tan φ = or x = h tan φ
⇒ = h sec2 φ
⇒ v = h sec2 φω
So putting values
h = 3, φ = 180 - (90 + 45) = 45o
we get v = × 0.1 = 0.6 m/s

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