A group of students have two carts, Cart 1 and Cart 2, each of known mass M1 and M2. The carts are placed on a straight horizontal track. Cart 1 is given an initial speed v0 toward Cart 2, which is at rest. Cart 1 collides with Cart 2. The students are tasked with determining the relationship between v0 and the fraction of kinetic energy remaining after the collision. Specifically, they must find the ratio of total final kinetic energy to total initial kinetic energy of both carts before and after the collision.