Question

The car maintains a constant speed of v=58 m/s. Determine the angular velocity ?̇ of the camera tracking the car when θ = 30.

r=(25sin?̇) meter

Answer 1

V = 58 m/s % - 25 sino Camera

From the above figure,

..............(1)

r=rtano

r = 25 $sin\theta$ = 25 sin(30) = 12.5 m

Differentiang equation (1)

.............(2)

dx/dt = rd(tand)/dt

dx/dt = V = 58 m/s

Substituting the values in eq.(2) we get,

$58 = 12.5 *{d(tan\theta )/d\theta} * (d\theta/dt)$

58 = 12.5 x $sec^{2}\theta$ x $\omega$

Angular velocity ($\omega$) = 3.48 rad/s