Respuesta :
We know that
• The mass of the ball is 10kg.
,• The initial velocity of the ball is 9m/s.
,• The mass of the man is 130kg.
,• The initial velocity of the man is null (stationary).
,• The final velocity of the ball is 5m/s.
To find the final velocity of the person, we have to use the law of conservation of momentum.
[tex]p_i=p_f[/tex]Where p = mv. Using all the given information, we have
[tex]\begin{gathered} m_{^{}_{ball}}v_{i_{ball}}+m_{_{man}}v_{i_{man}}=m_{\text{ball}}v_{f_{ball}}+m_{man}v_{f_{man}}_{} \\ 10\operatorname{kg}\cdot9m/s+130\operatorname{kg}\cdot0=10\operatorname{kg}\cdot5m/s_{}_{}+130\operatorname{kg}\cdot v_{f_{man}} \end{gathered}[/tex]Then, we solve for v
[tex]\begin{gathered} 90\operatorname{kg}\cdot m/s=50\operatorname{kg}\cdot m/s+130\operatorname{kg}\cdot v_{f_{man}} \\ \frac{90\operatorname{kg}\cdot m/s-50\operatorname{kg}\cdot m/s}{130\operatorname{kg}}=v_{f_{man}} \\ v_{f_{man}}=\frac{40\operatorname{kg}\cdot m/s}{130\operatorname{kg}}\approx0.31m/s \end{gathered}[/tex]Therefore, the velocity of the person after the ball bounces off him is 0.31 meters per second, approximately.
