In order to determine the final velocity of the system, the scientist must use the conservation of momentum equation: m1v1 + m2v2 = (m1 + m2)vf. This equation takes into account the masses and velocities of both the cart and wagon before and after the collision.
The collision can be classified as elastic or inelastic by calculating the coefficient of restitution, which is a measure of the relative velocities before and after the collision. If the coefficient of restitution is equal to 1, the collision is elastic. If it is less than 1, the collision is inelastic.
The direction of the final velocity can be determined by using the conservation of momentum equation. The direction of the final velocity will be in the same direction as the initial velocity of the lighter object, in this case the cart.
Before the collision, the total momentum of the system will be equal to the sum of the individual momenta of the cart and wagon. After the collision, the total momentum of the system will still be equal to the sum of the individual momenta, as momentum is conserved in a closed system.
The mass of the objects will affect the outcome of the collision by determining how much momentum each object has. The heavier object will have more momentum and will therefore exert a greater force on the lighter object during the collision. This will result in a change in the velocity of both objects after the collision.