The law of conservation of momentum says that the total momentum in the system before and after the collision remains the same. Remember that <em>p = mv </em>(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)
