Two frictionless roller-coaster cars sit atop identical roller coaster tracks. The two roller-coasters meet at the bottom to form a single continuous roller-coaster track. The more massive car has mass M, the less massive has mass m. Neglect air resistance.
a) If the two cars are released simultaneously from rest, describe in words where the two cars collide.
b) If when they collide, the two cars stick together, calculate the highest height the two cars will ultimately reach after they stick together, expressed in relation to their original height.