An astronaut in a space suit is motionless in outer space.The propulsion unit strapped to her back ejects some gas with a velocity of 50 m/s.The astronaut recoils with a velocity of 1.0 m/s.If the mass of the astronaut and space suit after the gas is ejected is 120 kg,the mass of the gas ejected is
A) 1.0 kg.
B) 1.9 kg.
C) 2.4 kg.
D) 3.00 kg.
E) 3.6 kg.

Question

Quizplus · Accepted Answer

According to conservation of momentum, the total momentum of the system (astronaut + gas) before the ejection is zero (since the astronaut is motionless). After ejection, the momentum of the astronaut and gas must still add up to zero. Let m be the mass of the gas ejected. Then:

momentum of gas = m x 50 m/s
momentum of astronaut = (m + 120 kg) x (-1.0 m/s)

Setting these two expressions equal (since total momentum must be zero):

m x 50 m/s = (m + 120 kg) x (-1.0 m/s)

Simplifying and solving for m:

50m = -m - 120

m = 2.4 kg

Therefore, the mass of gas ejected is 2.4 kg. The answer is C.

An Astronaut in a Space Suit Is Motionless in Outer