**a.**

Law of conservation of momentum.

$\overline{){\mathbf{m}}{{\mathbf{v}}}_{{\mathbf{0}}}{\mathbf{=}}{\mathbf{m}}{{\mathbf{v}}}_{{\mathbf{f}}}}$

Solving:

$\begin{array}{rcl}{\mathbf{m}}_{\mathbf{b}}{\mathbf{v}}_{\mathbf{0}\mathit{b}}& \mathbf{=}& \mathbf{(}{\mathbf{m}}_{\mathbf{b}}\mathbf{+}{\mathit{m}}_{\mathbf{O}}\mathbf{)}{\mathbf{v}}_{\mathbf{f}}\\ {\mathbf{v}}_{\mathbf{f}}& \mathbf{=}& \frac{{\mathbf{m}}_{\mathbf{b}}{\mathbf{v}}_{\mathbf{0}\mathit{b}}}{{\mathbf{m}}_{\mathbf{b}}\mathbf{+}{\mathit{m}}_{\mathbf{O}}}\end{array}$

a. If Olaf catches the ball, initially moving at a speed of 10.8 m / s, with what speed v_{f }do Olaf and the ball move afterward? Olaf's mass is 70kg and the ball's mass is 0.4kg. Express your answer numerically in centimeters per second.

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

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