Answer: 5.9 m/s
Explanation:
This problem can be solved by the Conservation of Momentum principle, which establishes that the initial momentum [tex]p_{o}[/tex] must be equal to the final momentum [tex]p_{f}[/tex]:
[tex]p_{o}=p_{f}[/tex] (1)
Where:
[tex]p_{o}=(m_{1}+m_{2})V_{o}[/tex] (2)
[tex]p_{f}=m_{1}U_{f}+m_{2}V_{f}[/tex] (3)
[tex]m_{1}=50 kg[/tex] is the mass of the skater
[tex]m_{2}=3 kg[/tex] is the mass of the ball
[tex]V_{o}=5 m/s[/tex] is the initial velocity of the skater and the ball
[tex]V_{f}=-10 m/s[/tex] is the final velocity of the ball
[tex]U_{f}[/tex] is the final velocity of the skater
Substituting (2) and (3) in (1):
[tex](m_{1}+m_{2})V_{o}=m_{1}U_{f}+m_{2}V_{f}[/tex] (4)
Isolating [tex]U_{f}[/tex]:
[tex]U_{f}=\frac{(m_{1}+m_{2})V_{o}-m_{2}V_{f}}{m_{1}}[/tex] (5)
[tex]U_{f}=\frac{(50 kg+3 kg)5 m/s}-(3 kg)(-10 m/s)}{50 kg}[/tex] (6)
Finally:
[tex]U_{f}=5.9 m/s[/tex]
