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 θ = 30°.

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 heta = 30°.

Accepted Answer

r=2(20)[latex]\cos { heta }[/latex] =40[latex]\cos { heta }[/latex]

[latex]\dot { r }[/latex] =-(40[latex]\sin { heta }[/latex] )[latex]\dot { heta }[/latex]

v = [latex]\dot { r }[/latex] [latex]{u}_{r}[/latex] + r[latex]\dot { heta }{u}_{ heta}[/latex]

v=[latex]\sqrt { ({ \dot { r } ) }^{ 2 }+ { (r\dot { heta } ) }^{ 2 } }[/latex]

[latex]{(30)}^{2}[/latex] =[latex]{ (-40\sin { heta })}^{2}[/latex][latex]{(\dot{ heta})}^{2}[/latex] + [latex]{(40\cos{ heta})}^{2}[/latex][latex]{(\dot{ heta})}^{2}[/latex]

[latex]{(30)}^{2}[/latex] = [latex]{(40)}^{2}[{\sin}^{2} heta[/latex]+[latex]{\cos}^{2} heta[/latex]] [latex]{(\dot{ heta})}^{2}[/latex]

[latex]\dot{ heta}[/latex] = [latex]\frac { 30 }{ 40 }[/latex] = 0.75 rad/s

Question : A cameraman standing at A is following the movement of a rac...

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