Question

A 685-kg car stopped at an intersection is rear-ended by a 1510-kg truck moving with a speed of 11.5 m/s. If the car was in neutral and its brakes were off, so that the collision is approximately elastic, find the final speed of both vehicles after the collision.

Answer 1

mt=truck's mass
vi=initial velocity of the truck
vf=final velocity of the truck

mc=car's mass
ci=initial velocity of the car (ci=0)
cf=final velocity of the truck

You have to use this:
Conservation of linear momentum: mc*ci+mt*vi=mc*cf+mt*vf
Conservation of kinetic energy: \[1/2(m_c)*c_i^2+1/2(m_t)*vi^2=1/2(m_c)*cf^2+1/2(m_t)*vf^2\]

Hope it helps.