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 magnitude 50 m/s. The astronaut recoils with a velocity of 1.0 m/s in the opposite direction. 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) 3.0 kg.
E) 3.6 kg.

Question

Quizplus · Accepted Answer

According to the law of conservation of momentum, the initial momentum of the system (astronaut + propulsion unit) is zero. After the gas is ejected, the total momentum of the system is still zero. Let the mass of gas ejected be m.

Therefore, 
Initial momentum = 0 
= Final momentum 
(mass of astronaut + propulsion unit) x (-1.0 m/s) + (mass of gas) x (50 m/s) = (mass of astronaut and space suit after gas is ejected) x velocity of astronaut and space suit 
(70 kg + 50 kg) x (-1.0 m/s) + m x (50 m/s) = 120 kg x unknown velocity 
-120 m/s + 50 m/s m = 120 kg x unknown velocity 
-70 m/s m = 120 kg x unknown velocity 
m = (120 kg x 1.0 m/s) / 70 m/s 
m = 1.7 kg 
Therefore, the mass of the gas ejected is approximately 2.4 kg (Option C).

An Astronaut in a Space Suit Is Motionless in Outer