## Precalculus (10th Edition)

$794.16$mph.
The distance from the axis is: $r=3033.5$ miles. The Earth takes $24$ hours to make a revolution, hence its angular velocity is: $\omega=\frac{2\pi}{t}=\frac{2\pi}{24}=0.2618\frac{\text{rad}}{\text{hr}}.$ Therefore the linear velocity at $40^\circ$: $v=\omega r\\v=0.2618(3033.5)=794.16\text{mph}$