A 85-kg astronaut (including spacesuit and equipment) is floating at rest a distance of 11 m from the spaceship when she runs out of oxygen and fuel to power her back to the spaceship. She removes her oxygen tank (3.0 kg) and flings it away from the ship at a speed of 15 m/s relative to the ship. A. At what speed relative to the ship does she recoil toward the spaceship? B. How long must she hold her breath before reaching the ship?

(A) Speed = 0.5294 m/s

(B) Time taken = 20.78 seconds

Explanation:

This question is solved by using conservation of momentum principles.

The momentum the astronaut provides the tank will also be applied on her in the opposite direction.

Thus, we have:

Momentum of tank = Speed  * Mass of tank

Momentum of tank = 15 * 3

Momentum of tank = 45   kg*m/s

So, the momentum of the astronaut will also be 45 kg*m/s.

(A) We calculate her speed as follows:

Momentum of astronaut = Speed * Mass of astronaut

45 = Speed * 85

Speed = 0.5294 m/s

(B) Distance of astronaut to ship = 11 meters

Time taken by astronaut to reach ship = distance / speed of astronaut

Time taken = 11 / 0.5294

Time taken = 20.78 seconds

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