Answer
(a) v = 464 m/s
(b) v = 185 m/s
(c) v = 345 m/s
Work Step by Step
$\omega = (1 \frac{rev}{day})(2\pi \frac{rad}{rev})(\frac{1~day}{24 \times 3600~s}) = \frac{\pi}{43200}~rad/s$
We can use 6380 km as the radius of the Earth.
Note that at a latitude of $\theta ^{\circ}$, the radius of rotation is $r = 6380~km\times cos(\theta ^{\circ})$.
(a) $v = \omega r = ( \frac{\pi}{43200}~rad/s)(6380~km)$
$v = 464~m/s$
(b) $v = \omega r = ( \frac{\pi}{43200}~rad/s)(6380~km\times cos(66.5^{\circ}))$
$v = 185~m/s$
(c) $v = \omega r = ( \frac{\pi}{43200}~rad/s)(6380~km\times cos(42.0^{\circ}))$
$v = 345~m/s$
