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 `

Answer

`0.6`

Explanation

` x= 3 tan beta`
`rArr v = (dx)/(dt) = 3 sec^2 beta (dbeta//dt)`
`rArr v_(beta=45^@) = 3(sec^245^@) xx 0.1 = 0.6 ms^(-1)`