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

Options

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

Answer

A

Explanation

Let x is the distance of point P from O, the from figure
`tan phi=x/h` or `x=htan phi`
`rArr (dx)/(dt)=h sec^(2) phi (d theta)/(dt)`
`[(dphi)/(dt)=omega]rArr v=h sec^(2) phi omega`
So putting values
`h=3, phi=180-(90+45)=45^(@)`
we get `v=(3sqrt(2))^(2)xx0.1=0.6 m//s`