## Question:

A cameraman standing at A is following the movement of a race car, B, which is traveling around a curved track at a constant speed of 30 m/s . Determine the angular rate at which the man must turn in order to keep the camera directed on the car at the instant $\theta$ = 30°.

## Step-by-step

r=2(20)$\cos { \theta }$ =40$\cos { \theta }$

$\dot { r }$ =-(40$\sin { \theta }$ )$\dot { \theta }$

v = $\dot { r }$ ${u}_{r}$ + r$\dot { \theta }{u}_{\theta}$

v=$\sqrt { ({ \dot { r } ) }^{ 2 }+ { (r\dot { \theta } ) }^{ 2 } }$

${(30)}^{2}$ =${ (-40\sin { \theta })}^{2}$${(\dot{\theta})}^{2}$ + ${(40\cos{\theta})}^{2}$${(\dot{\theta})}^{2}$

${(30)}^{2}$ = ${(40)}^{2}[{\sin}^{2}\theta$+${\cos}^{2}\theta$] ${(\dot{\theta})}^{2}$

$\dot{\theta}$ = $\frac { 30 }{ 40 }$  = 0.75 rad/s