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

The velocity `(v)` of spot `= dx//dt`
and the angular speed `( omega )` of spot light `= (d phi)/(dt)`
From `Delta SOP `,
`tan phi = (x)/(h)` `:. x = h tan phi`
`:. (dx)/(dt) = h sec^(2) phi (d phi)/(dt)` `:. v = ( h sec^(2) phi ) omega`
`:. v = 3 sec^(2) 45(@) xx 0.1` `[because theta + phi = 90(@) ]`
`:. v = 3 xx 2xx 0.1 = 0.6 m//s`