Question

The moon has a mass of 7.35 x 10^22 kg and a radius of 1.738 x 10^6 m. At what speed must a rocket be launched from the moon's surface so as not to fall back to moon.

Answer 1

We can find the escape velocity of the rocket as follows:

$$v=\sqrt{\dfrac{2GM}{r}},$$ $$v=\sqrt{\dfrac{2\times6.67\times10^{-11}\ \dfrac{N\times m^2}{kg^2}\times7.35\times10^{22}\ kg}{1.738\times10^6\ m}},$$ $$v=2380\ \dfrac{m}{s}=2.38\ \dfrac{km}{s}.$$