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.How far has the heavier astronaut moved when the lighter astronaut has moved 12 m?
A)16 m
B)9.0 m
C)21 m
D)7.0 m
E)12 m

Question

Quizplus · Accepted Answer

According to the conservation of momentum, the center of mass of the system remains constant if no external forces act on it. Since both astronauts push each other with equal and opposite forces, their momenta are equal in magnitude but opposite in direction. The distance moved by each astronaut is inversely proportional to their mass. If the lighter astronaut (60 kg) moves 12 m, the heavier astronaut (80 kg) will move a shorter distance because $ \frac{Distance_{heavier}}{Distance_{lighter}} = \frac{Mass_{lighter}}{Mass_{heavier}} $. Therefore, $ Distance_{heavier} = \frac{60}{80} \times 12 = \frac{3}{4} \times 12 = 9 $ meters.

Two Astronauts,of Masses 60 Kg and 80 Kg,are Initially Right