If Olaf catches the ball, with what speed vf do Olaf and the ball move afterward?

convervation
momentum

#1

1) If Olaf catches the ball, with what speed vf do Olaf and the ball move afterward?
Express your answer numerically in centimeters per second.

2) If the ball hits Olaf and bounces off his chest horizontally at 7.70 m/s in the opposite direction, what is his speed vf after the collision?
Express your answer numerically in centimeters per second.

Answer:

(1).mass of ball m = 0.4 kg
initial speed of the ball u = 10.8 m / s
let the mass of Olaf be M = 70 kg
from law of conservation of momentum , mu = ( m+ M ) v
from this speed of the Olaf and the ball move afterwards v = mu / ( m+ M)
= 0.06136 m / s
= 6.136 cm / s

(2).initial speed of the ball u = 10.8 m / s
initial speed of Olaf U = 0
speed of the ball after collision v = -7.7 m / s
speed of the Olaf after collision V = ?
from law of conservation of momentum ,
mu + MU = mv + MV
mu = mv + MV
MV = mu - mv
= m( u - v)
= 0.4 * 18.5
= 7.4 m / s
V = 7.4 / M = 7.4 / 70
= 0.1057 m / s
= 10.57 cm / s