Figure shows a torch producting a straight light beam falling on a plane mirror at an angle `60^(@)` The reflected beam makes a spot P on the screen along y-axis . If at t=0, mirror starts ratating about the hinge A with an angular velocity `(omega)=1^(@)` per second clockwise. Find the speed of the spot on screen after time t = 15 s.

Answer

A, B

Explanation

In 15 second, mirror will rotate `15^(@)` in clockwise direction.
Hence, the reflected ray will rotate `(30^(@))` in clockwise direction


`y=3 tan(theta)`
` :. (dy)/(dt)=(3 sec^(2) theta).(d theta)/(dt)` ...(i)
Here, `(dy)/(dt) =(v_(p)),(d theta)/(dt) =2^(@)` per second
`=(2xxpi)/(180)=(pi)/(90)` rad per second
At `t=15 s` and `(theta)=60^(@)`
Substituting the values in Eq. (i), we have
`v_(p)={3 sec^(2) 60^(@)}{(pi)/(90)}`
`=3xx4xx(pi)/(90)`
`=(2 pi)/(15) m//s`.