Spotlight `S` rotates in a horizontal plane with constant angular velocity of `0.1 ` radian //second`. The spot of light `p` moves along the wall at a distance of `3 m ` . The velocity of the spot `p` when `theta = 45(@)` (see - fig. ) is ……….. ` m//s `

Explanation

If `x` is the distance `P` and `O`
`tan alpha=(x)/(3)`
`x=3tanalpha`
`(dx)/(dt)=3 sec^(2)alpha(dalpha)/(dt)`
`v=3sec^(2)alpha omega`
`v=(dx)/(dt):"velocity of" P`
`omega=(dalpha)/(dt): "angular velocity of" S`
when `theta=45^(@),theta+alpha=90^(@)impliesalpha=45^(@)`
`omega=0.1 rad//s`
`v=3 sec^(2) 45^(@)xx0.1=3xx2xx0.1=0.6m//s`