Answer
(a) $75\ ft$
(b) $\frac{\pi}{45}\ rad/sec$
Work Step by Step
See diagram, given $r=50.0\ ft$ and $\theta=\frac{2\pi}{3}$, we have:
(a) The height of point P is $h=r+r\ sin(\theta-\frac{\pi}{2})=50+50sin(\frac{\pi}{6})=50+25=75\ ft$
(b) As it takes $30\ sec$ to turn an angle of $\frac{2\pi}{3}$, we have the angular speed as $\omega=\frac{\frac{2\pi}{3}}{30}=\frac{\pi}{45}\ rad/sec$
