A rod `AB` is moving on a fixed circle of radius `R=5m` with constant velocity `v=4m//s` as shown in figure. `P` is the point of intersection of the rod and the circle. At an instant the rod is at a distance `x=(3R)/5` from center of the circle. The velocity of the rodf is perpendicular to its lenght and the rod is always paraller to the diameter `(CD)`
Speed of point of intersection `P` is

Explanation

Let `P` have co-ordiantes `(x,y)`
`x=R cos theta,y= R sin theta`
`V_(x)=R sin theta(d theta)/(dt),(d theta)/(dt)=(-v)/(R sin theta)`
`V_(y)=R cos theta(d theta)/(dt)=R cos theta((-v)/(Rsin theta))`
`=-v cot theta`
`v_(p)=sqrt(v_(x)^(2)+v_(y)^(2))`