Question

A 50 kg Astronaut is floating in space, at rest relative to her spaceship. The 5kg canister she used for getting around has run out of gas. To get back to the spaceship she decides to throw the canister in the opposite direction.
a) What is the total momentum of the astronaut-canister system after the throw (relative to the spaceship)?
b) If the canister moves away at a speed of 20 m/s, what is the Astronaut’s speed toward the spaceship?

Answer 1

The initial speed of the astronaut u=0 m/s.

The mass of the astronaut is  M=50 kg.

The mass of the canister is m= 5 kg.

Let the total momentum of the system is P.

From the conservation of the momentum the momentum after and before throw the canister is equal.

The total momentum of the system is after the throw 0 N.s.

b) Let the Astronaut’s speed toward the spaceship is v2.

The speed of the canister v1=20 m/s.

From the conservation of momentum

  

  

The Astronaut’s speed toward the spaceship is 2 m/s.