Tubby and his twin brother Libby have a combined mass of 200 kg and are zooming along in a 100 kg amusement park bumper car at 10 m/s. They bump into flubbys bumper car which is stationary. Flubby is 25 kg in mass and his car is also 100 kg in mass. After the elastic collision, tubby and Lubby continue to move in the same direction but their speed is lessened from 10 m/s to 4.12 m/s. How fast is flubbys car moving?

We can solve this with the Conservation of Linear Momentum principle, which states the initial momentum [tex]p_{i}[/tex] (before the elastic collision) must be equal to the final momentum [tex]p_{f}[/tex] (after the elastic collision):

[tex]p_{i}=p_{f}[/tex] (1)

Being:

[tex]p_{i}=m_{1}V_{i} + m_{2}U_{i}[/tex]

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

Where:

[tex]m_{1}=200 kg +100 kg=300 kg[/tex] is the combined mass of Tubby and Libby with the car

[tex]V_{i}=10 m/s[/tex] is the velocity of Tubby and Libby with the car before the collision

[tex]m_{2}=25 kg + 100 kg=125 kg[/tex] is the combined mass of Flubby with its car

[tex]U_{i}=0 m/s[/tex] is the velocity of Flubby with the car before the collision

[tex]V_{f}=4.12 m/s[/tex] is the velocity of Tubby and Libby with the car after the collision

[tex]U_{f}[/tex] is the velocity of Flubby with the car after the collision

So, we have the following:

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

Finding [tex]U_{f}[/tex]:

[tex]U_{f}=\frac{m_{1}(V_{i}-V_{f})}{m_{2}}[/tex] (3)

[tex]U_{f}=\frac{300 kg(10 m/s-4.12 m/s)}{125 kg}[/tex] (4)

Finally:

[tex]U_{f}=14.1 m/s[/tex]