An astronaut is floating in space when the support line is cut. If the 68kg astronaut needs to reach the spaceship (20m away), how long will it take if he throws a 12kg canister at 12m/s?

Answer: 9.43 s

Explanation:

Since there is no external force acting in space, the total momentum of the entire system would be conserved.

When the astronaut throws a canister, an equal and opposite amount of force would act on the astronaut which means momentum of the canister would be equal to momentum of the astronaut,

⇒ m v = m' v'

⇒ 12 kg * 12 m/s = 68 kg * v'

The velocity of the astronaut would be:

v' = 2.12 m/s

The distance need to be covered by astronaut to reach the spaceship = 20 m

Time taken : Distance / velocity = 20 m / 2.12 m/s = 9.43 s.

Hence, astronaut would take 9.43 s to reach the spaceship.