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

taking radial direction along i then

v_ascent = 1.7 m/s i

and tengential velocity will be perpendicular to it.

Applying momentum conservation along i direction,

2600 x 1.7 = (2600 + 4500) v

v = 0.62 m/s

So radial component will be 0.62 m/s ........Ans

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