The distance traveled from this point depends on the height. Therefore, the total distance traveled equals the distance crossed in going 1.22 seconds at the original x velocity plus the distance traveled going for 1.22 seconds at the velocity after the collision. Since the bullet velocity is given with respect to a stationary observer, we can get the velocity of the cart from momentum conservation by using velocities relative to a stationary observer . Let the direction of the bullet be the positive direction. Since the momentum of the bullet is transferred back to the block, we go back to a situation in which the momentum of the block, gun, and bullet are all zero.
L is the distance the block travels.
To get the distance traveled by the block, we need to consider the relative velocity of the bullet with respect to the block. Then the kinetic energy in this frame is K tot. The velocities relative to the center of mass are v 1, rel. The relative kinetic energies are K 1, rel. K 1, rel.