On Apollo Moon missions, the lunar module would blast off from the Moon\'s surfa

Question

On Apollo Moon missions, the lunar module would blast off from the Moon's surface and dock with the command module in lunar orbit. After docking, the lunar module would be jettisoned and allowed to crash back onto the lunar surface. Seismometers placed on the Moon's surface by the astronauts would then pick up the resulting seismic waves.

Find the impact speed of the lunar module, given that it is jettisoned from an orbit 160km above the lunar surface moving with a speed of 1700m/s . (Please inlcude an answer, thank you)

Explanation / Answer

This i a simple question, but i'd just like to highlight that we are assuming that the lunar module is within the HIll sphere (technical term for gravitational sphere of influence) of the moon so that we can disregard the other big bodies like the earth and the sun, when we do our calculations:

conservation of energy:

(1/2)m(v_f^2- v_i^2)=m g_moon*h
-->(1/2)*(1700^2 -v_i^2)=1.6*160

v_i=1699.85 m/s

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