8. Determine the desired quantity in each of the followingcollisions: (a) A student of mass 60kg sits on a rolling chair(assume no friction with the ground). He pulls out a fireextinguisher and fires 2kg of material at a velocity of 8m/s. Howfast is he moving after this process? (b) A 90kg astronaut istraveling through space at a rate of 2m/s. He is holding a 5kg massas he travels. How fast would he have to throw this mass in orderto come to rest? (c) A box of mass 20kg slides across an icy floorat a rate of 5m/s. In order to stop it, we slide smaller boxes ofmass of 0.8kg towards it at a rate of 1m/s. How many boxes mustcollide with (and stick to) it before it comes to a stop? (d) Afootball player with mass 70kg runs towards another at a rate of4m/s. Realizing he’s about to get walloped, the second player runstowards the first at a rate of 2m/s. If the second player has amass of only 50kg, what is the velocity of the pair after thecollision? (e) Three billiard balls travel along a table. The firstis moving rightwards with a speed of 2m/s, the second is movingleftwards with a speed of 2m/s, and the middle one lies halfwaybetween the first two. What is the velocity of the ball in themiddle after the collision?

(f) Alice, with a mass of 60kg, jumps upwards off the Earth. Atthe moment of her jump, how fast does she move the Earth in theopposite direction? (The mass of the earth is about 5.972 ·1024kg)