A racing car is travelling along a straight track at a constant velocity of `40m//s`. A fixed TV camera is recording the even as shown in figure. In order to keep the car in view in the position shown the angular velocity of camera should be

Options

A. `(a)3rad//s`
B. `(b)2rad//s`
C. `(c)4rad//s`
D. `(d)1rad//s`

Explanation

`x=30tantheta`
`therefore((dX)/(dt))=(30sec^(2)theta).(dtheta)/(dt)`
or `v_(car)=(30sec^(2)theta)omega`
`thereforeomega=(v_(car))/(30sec^(2)theta)`
`=(40)/((30)sec^(2)30^(@))=1rad//s`