On April 11, 1970, Apollo 13 was launched at Kennedy Space Flight center, Florid

Question

On April 11, 1970, Apollo 13 was launched at Kennedy Space Flight center, Florida LC 39A. Appollo 13 carried Astronaunts James A. Lovel, John L Swigert, and Fred W. Haise on their voyage to the moon. However, two days into the flight and 321,860 km from Earth when stirring the oxygen tanks, the Teflon-insulated wires that provided electricity to the stirrer motor were damaged, causing a large fire when electricity passed through them. The fire heated the surrounding oxygen, increasing the pressure inside the tank above its 1000 PSI limit, causing the tanks to explode. This explosion caused Apollo 13 to abandon its moon voyage and to try return back to Earth. To return to Earth, the astronaunts aboard Apollo 13 used the moon to slingshot them back to Earth. The spacecraft had a total mass 68,000 kg (including the 1775.1 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

Mass = 68000 kg

Since 1 miles per hour = 0.44704 meters per second

Initial velocity = -24000 mph = -10728.96 m/s

Final velocity = +24000 mph = = +10728.96 m/s

Force(thrust) = 689 kN = 689000 N

Momentum = mass x velocity

Force (thrust) = change in momentum/time

= (final momentum - initial momentum)/time

689000 = (68000 x 10728.96 - 68000 x (-10728.96))/time

Time = 2118 s = 0.588 hours

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