A child of mass 25 kg is skating fast, +10 m/s, and tries to get revenge by colliding with the 60 kg adult who is sitting still. After the collision, the adult goes forward at 6 m/s. What is the child's final velocity?

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}V_{o}+m_{2}U_{o}[/tex] (2)

[tex]p_{f}=m_{1}V_{f}+m_{2}U_{f}[/tex] (3)

[tex]m_{1}=25 kg[/tex] is the mass of the child

[tex]V_{o}=10 m/s[/tex] is the initial velocity of the child

[tex]m_{2}=60 kg[/tex] is the mass of the adult

[tex]U_{o}=0 m/s[/tex] is the initial velocity of the adult (it is sitting still)

[tex]V_{f}[/tex] is the final velocity of the child

[tex]U_{f}=6 m/s[/tex] is the final velocity of the adult

Substituting (2) and (3) in (1):

[tex]m_{1}V_{o}+m_{2}U_{o}=m_{1}V_{f}+m_{2}U_{f}[/tex] (4)

Isolating [tex]V_{f}[/tex]:

[tex]V_{f}=\frac{m_{1}V_{o}-m_{2}U_{f}}{m_{1}}[/tex] (5)

[tex]V_{f}=\frac{(25 kg)(10 m/s)-(60 kg)(6 m/s)}{25 kg}[/tex] (6)

Finally:

[tex]V_{f}=-4.4 m/s[/tex] This means the velocity of the child is in the opposite direction