Two astronauts, of masses 60 kg and 80 kg, are initially right next to each other and at rest in outer space. They suddenly push each other apart. What is their separation after the heavier astronaut has moved 12 m?
A) 28 m
B) 24 m
C) 9.0 m
D) 16 m
E) 21 m

Question

Two astronauts, of masses  60 kg and  80 kg, are initially right next to each other and at rest in outer space. They suddenly push each other apart. What is their separation after the heavier astronaut has moved  12 m?
A)  28 m
B)  24 m
C)  9.0 m
D)  16 m
E)  21 m

Quizplus · Accepted Answer

The principle of conservation of momentum states that the total momentum of a closed system is constant if no external forces are acting on it. Since both astronauts push each other away with equal and opposite forces and start from rest, their momenta are equal in magnitude but opposite in direction. Let $d$ be the distance the lighter astronaut moves. The ratio of their distances moved is inversely proportional to their masses, so $\frac{d}{12} = \frac{80}{60}$ or $d = 16$. Their separation is the sum of the distances they both moved, which is $12 + 16 = 28$ meters.

Two Astronauts, of Masses 60 Kg and 80