A spot light `S` rotates in a horizontal plane with a constant angular velocity of `0.1 rad//s`. The spot of light `P` move along the wall at a disatnce `3 m`. What is the velocity of the spot `P` when `theta = 45^(@)` ?

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`