Answer
$2291.94\text{mph}$
Work Step by Step
The distance from the Moon to the Earth is: $r=2.39\cdot10^5$ miles.
The Moon takes $27.3$ days($=27.3\cdot24$ hours) to make a revolution, hence its angular velocity is: $\omega=\frac{2\pi}{t}=\frac{2\pi}{27.3\cdot24}=9.589\cdot10^{-3}\frac{\text{rad}}{\text{hr}}.$
Therefore the linear velocity at $40^\circ$:
$v=\omega r\\v=9.589\cdot10^{-3}(2.39\cdot10^5)=2291.94\text{mph}$
