1. An 80.0-kg astronaut is floating at rest a distance of 10.0 m from a 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 into space away from the ship with a speed of 15 m/s. At what speed does she recoil toward the spaceship?

Question

1.	An 80.0-kg astronaut is floating at rest a distance of 10.0 m from a 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 into space away from the ship with a speed of 15 m/s. At what speed does she recoil toward the spaceship? 
2.	An 0.08-kg arrow moving at 80.0 m/s hits and embeds in a 10.0-kg block resting on ice. Use the conservation-of-momentum principle to determine the speed of the block and arrow just after the collision.

Sancho · Answer

In the of conservation of momentum if 2 objects collide and recoils or bounces from each other, they must have the same amount of momentum.
The momentum of the oxygen tank is 3.0kg x 15 m/s = 45. The Austronoaut should have the same momentum by dividing her mass with the momentum of the tank which is 80/45 is .5625 m/s.
.5625 is the velocity of the austronet during or after her recoil and if you try to get her momentum by multiplying her mass and velocity, it would turn out to be 45 units of mementum, becuse the system made should have the same momentum for each object colliding and using the law to conservation of momentum conserve it or equalize it.