Answer:
[tex]a)v_{f}=0.88m/s[/tex]
Explanation:
To solve this problem we use the Momentum's conservation Law, before and after the girl catch the ball:
[tex]\\ p_{1}=p_{2}\\m_{ball}*v_{o.ball}+m_{girl}*v_{o.girl} = m_{ball}*v_{f.ball} + m_{girl}*v_{f.girl} [/tex] (1)
At the beginning the girl is stationary:
[tex]v_{o.girl}=0m/s[/tex] (2)
If the girl catch the ball, both have the same speed:
[tex]v_{f.girl}=v_{f.ball}=v_{f}[/tex] (3)
We replace (2) and (3) in (1):
[tex]m_{ball}*v_{o.ball} = (m_{ball}+m_{girl})*v_{f} \\ [/tex]
We can now solve the equation for v_{f}:
[tex]v_{f}=\frac{m_{ball}*v_{o.ball}}{(m_{ball}+m_{girl})}=\frac{15*4.7}{15+65}=0.88m/s[/tex]
