After completing their moon-exploration mission, the two astronauts forming the crew of an Apollo lunar excursion module

Question:

After completing their moon-exploration mission, the two astronauts forming the crew of an Apollo lunar excursion module (LEM) would prepare to rejoin the command module which was orbiting the moon at an altitude of 140 km. They would fire the LEM??s engine, bring it along a curved path to a point A, 8 km above the moon??s surface, and shut off the engine. Knowing that the LEM was moving at that time in a direction parallel to the moon??s surface and that it then coasted along an elliptic path to a rendezvous at B with the command module, determine

(a) The speed of the LEM at engine shutoff,

(b) the relative velocity with which the command module approached the LEM at B. (The radius of the moon is 1740 km and its mass is 0.01230 times the mass of the earth.)