A 1.5 kg cart traveling at 1.2 m/s hits and bounces off a 0.75 kg cart that was at rest. The 0.75 kg cart moves forward at 2.0 m/s. How fast does the first cart end up going?

The law of conservation of momentum says that the total momentum in the system before and after the collision remains the same. Remember that p = mv (where p is momentum, m is mass, and v is velocity). To find the total momentum in the system, add up the momentum of each component.

Before the collision:

The momentum of the first cart is m*v = 1.5 * 1.2 = 1.8.

The momentum of the second cart is m*v = 0.75 * 0 = 0.

The total momentum is 1.8.

After the collision:

(where x is the unknown velocity):

The momentum of the first cart is m*v = 1.5x

The momentum of the second card is m*v = 0.75 * 2 = 1.5.

The total momentum is 1.5x + 1.5. Because of conservation of momentum, you know this is equal to the momentum before the collision:

1.8 = 1.5x + 1.5

Subtracting 1.5 from both sides:

0.3 = 1.5x

And dividing by 1.5:

x = 0.2 m/s forward (you know it is forward because it is positive)