Question

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?

Answer 1

Answer: -4.4 m/s

Explanation:

This problem can be solved by the Conservation of Momentum principle, which establishes that the initial momentum $p_{o}$ must be equal to the final momentum $p_{f}$:

$p_{o}=p_{f}$ (1)

Where:

$p_{o}=m_{1}V_{o}+m_{2}U_{o}$ (2)

$p_{f}=m_{1}V_{f}+m_{2}U_{f}$ (3)

$m_{1}=25 kg$ is the mass of the child

$V_{o}=10 m/s$ is the initial velocity of the child

$m_{2}=60 kg$ is the mass of the adult

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

$V_{f}$ is the final velocity of the child

$U_{f}=6 m/s$ is the final velocity of the adult

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

$m_{1}V_{o}+m_{2}U_{o}=m_{1}V_{f}+m_{2}U_{f}$ (4)

Isolating $V_{f}$:

$V_{f}=\frac{m_{1}V_{o}-m_{2}U_{f}}{m_{1}}$ (5)

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

Finally:

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