When leaving the moon, Apollo astronauts blasted off in an ascent module that do

Question

When leaving the moon, Apollo astronauts blasted off in an ascent module that docked with the command module (meaning they joined together while in flight while the command module was orbiting the moon in a circular orbit with a speed of 1.5 km/s. The ascent module had a mass of 2600 kg and approached the command module from below with a relative velocity of 1.7 m/s in the radial direction. The command module had a mass of 4500 kg. What is the radial component of the command module's velocity after the ascent module docks with it?

Explanation / Answer

The acsent module is perpendicular to the command module at the time of docking and the command module has only tangential velocity 1.7 m/s and no radial velocity

conserving the total momentum in radial direction

momentum before docking pi = 26000*1.7 kg-m/s

momentum after docking pf     = (26000+45000) * vf

(26000+45000) * vf = 26000*1.7

final radial velocity after docking vf = 26000*1.7 /45000 = 0.98 m/s

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