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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

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