Question

A satellite (pictured in brown) of mass 4000kg is in a circular orbit around the earth at a distance 6Re from the earth's center (Reis the earth's radius which is about 6.37×10^6. Another satellite (pictured in grey) of the same mass as the first and traveling faster but going in the same direction, crashes into it as shown. After the crash, the two objects stick together. What velocity must the second grey satellite have, right before the collision, in order that the two objects end up escaping from the earth's gravitational field? (Don't forget that the acceleration due to gravity at r=Re is g=9.81ms2.. If you do the problem using symbols instead of numerical values as far as possible, you can use this information to simplify your equations.)

Answer 1