Answer
(a) $v = 418~m/s$
(b) $v = 197~m/s$
Work Step by Step
We can find the angular speed of the earth as it rotates once each day:
$\omega = \frac{2\pi~rad}{(24)(3600~s)}$
$\omega = 7.27\times 10^{-5}~rad/s$
Note that for a point on the earth's surface at a latitude of $\theta$, the radius of rotation is $(6.4\times 10^6~m)~cos(\theta)$
(a) $v = \omega ~r$
$v = (7.27\times 10^{-5}~rad/s)(6.4\times 10^6~m)~cos(26^{\circ})$
$v = 418~m/s$
(b) $v = \omega ~r$
$v = (7.27\times 10^{-5}~rad/s)(6.4\times 10^6~m)~cos(65^{\circ})$
$v = 197~m/s$
