Two astronauts, with masses 60. and 80. kg, are initially at rest in outer space. They push each other apart. How far has the heavier astronaut moved when the lighter astronaut has moved 12. m?
A) 7.0 m
B) 21. m
C) 16. m
D) 12. m
E) 9.0 m

Question

Quizplus · Accepted Answer

The conservation of momentum principle states that the total momentum of a closed system is constant if no external forces are acting on it. In this scenario, the system of two astronauts is closed and isolated in space, meaning their combined momentum remains zero as they push away from each other. Since momentum is the product of mass and velocity (p = mv), and both astronauts start from rest and exert equal and opposite forces on each other, their momenta are equal in magnitude but opposite in direction. Therefore, the ratio of their distances moved is inversely proportional to their masses. For the heavier astronaut (80 kg) and the lighter astronaut (60 kg) who moves 12 m, the distances they move are inversely proportional to their masses: $ \frac{60}{80} = \frac{12}{d} $, solving for $d$ gives $d = 9.0$ m.

Two Astronauts, with Masses 60