Answer
The linear speed at Salem is $1185~km/hr$
Work Step by Step
The earth rotates through an angle of $2\pi$ radians in 24 hours. We can find the angular speed:
$\omega = \frac{2\pi~rad}{24~hrs}$
$\omega = \frac{\pi~rad}{12~hrs}$
$\omega = 0.2618~rad/hr$
The angular speed is $0.2618~rad/hr$
At a point halfway between the equator and the North Pole, we can find the radius of rotation $r$:
$\frac{r}{6400~km} = sin ~45^{\circ}$
$r = (6400~km) (sin ~45^{\circ})$
$r = 4525~km$
We can find the linear speed at Salem:
$v = \omega ~r$
$v = (0.2618~rad/hr)(4525~km)$
$v = 1185~km/hr$
The linear speed at Salem is $1185~km/hr$
