You are standing on a sheet of ice that covers the football stadium parking lot in Buffalo; there is negligible friction between your feet and the ice. A friend throws you a ball of mass 0.400kg that is traveling horizontally at 10.5m/s . Your mass is 70.0 kg
A)If you catch the ball, with what speed do you and the ball move afterwards?
B)If the ball hits you and bounces off your chest, so afterwards it is moving horizontally at 8.50 in the opposite direction, what is your speed after the collision?
2 Answers

In both cases you just have to use one fundamental. Law of conservation of momentum.
Mass of ball*vel. of ball = (Mass of ball and mass of body) * Speed of combined body(since they are now together)
1. 0.4 * 10.5 = (70 + 0.4) * Speed
Solve for speed
2. 0.4 * 10.5 = 0.4 *8.5 + 70*Speed
Solve for speed

Using the law of cons. of momentum
initial = 0.4kg x 10.5m/s
final = (70 + 0.4)kg x V
► ............... V = 0.4 x 10.5 /70.4 = ..☺
B) involves conservation taking account of directions (ans. No 1 hasn't ! )
initial = 0.4 x 10.5 = 4.2 kgm/s
final = (70kg x V→) + (0.4kg x 8.5←) = 70V  3.4
now .. 4.2 = 70V  3.4 .............► V = 7.6 /70 = 0.109 m/s