**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