A rocket launches from the surface of Earth with a speed twice the escape speed of Earth. When it is very far from Earth, what is its speed?

surface-of-earth

#1

A rocket launches from the surface of Earth with a speed twice the escape speed of Earth. When it is very far from Earth, what is its speed?

Answer:

The rocket has an initial speed that is twice the escape speed, that is approximately 22.4km/s. The rocket also has kinetic energy that is four times greater than that required to escape.

Thus, once the rocket has escaped, the kinetic energy is three times the escape energy.

As such, the speed is √3 (= 1.732) times the escape speed, which is approximately, 19.4km/s.