321,860 km from Earth, astronaunts aboard Apollo 13 used the moon to slingshot t

Question

321,860 km from Earth, astronaunts aboard Apollo 13 used the moon to slingshot them back to Earth. The spacecraft had a total mass 68,000 kg (including the 1835.9 kg of fuel and the 3 astronaunts) and was capable of producing 689 kN of thrust. Using this information, determine how long it would take for the Astronaunts traveling at 24,000 mph to perform an emergency burn and return to Earth traveling at 24,000 mph. In other words, how long would it take the Apollo spacecraft to go from 24,000 mph in one direction to 24,000 mph in the other direction. Note: Make time positive.

Explanation / Answer

24000 mph = 10728.96 m/s

first leg: going from 24000 mph to 0

v = v0 - at

a = F / m

t = (v0 - v)/a = v0 m / F = 10728.96 * 68000 / 689*1000 = 1059 s

it takes another 1059 s to accelerate from 0 to 24000 mph

so total time = 2*1059 = 2118 s

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