Figure shows a torch producing 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.

Explanation

When incident ray is fixed the angular velocity of reflected ray becomes twice in the same sense as that of reflected ray. After t = sec, the mirror rotates `15^(@)` then reflected ray rotates `30^(@)` in the same sense.
cos`60^(@) = 3/r, omega=1 degree per`
sec = `pi/180` rad/sec. r = 6m
Then, there are two components of velocity of spot on the screen
(i) Perpendicular component `V_(s)cos 60^(@)=2omega r implies V_(s)xx1/2 = 2xxpi/180xx6`
`implies V_(s)= (2pi)/15` m/s
(ii) radial component which increases the length of r i.e `V_(s) sin 60^(@) = (dr)/(dt)`