An astronaut of mass m emerged from the hatch of the spacecraft, and, pushing off from the spacecraft

An astronaut of mass m emerged from the hatch of the spacecraft, and, pushing off from the spacecraft, acquired a speed of v. What speed has the spacecraft acquired as a result of this interaction if its mass is 100 times the mass of the astronaut?

Given:

m is the mass of the astronaut leaving the spacecraft;

M = 100 * m is the mass of the spacecraft;

v is the cosmonaut’s speed, which he acquired by pushing off from the spacecraft.

It is required to determine V – the speed of the spacecraft as a result of interaction with the astronaut.

According to the law of conservation of momentum (momentum):

m * v = M * V

V = m * v / M = m * v / (100 * m) = v / 100 = 0.01 * v.

Answer: as a result of interaction with the cosmonaut, the spacecraft acquired a speed equal to 0.01 * v.