Answer to Question #169002 in Physics for Monica

Question

A spoon rides a roller coaster at the fair. He and his car have a mass of 500.0 kg and coast down a 100 m hill from rest. At the bottom of the hill he (and her car) collide with a car and riders, a ghost and a calf (m=850kg), that sit at rest. If the collision is elastic, will the ghost and the calf make it over the hill that is 50.0 m high?

Answer 1

$$mv=-mv'+Mu\\m\sqrt{2gH}=-mv'+Mu$$

$$u=\frac{2m}{m+M}\sqrt{2gH}\\ u=\frac{2(500)}{500+850}\sqrt{2(9.8)(100)}=32.8\frac{m}{s}$$

And the needed speed will be

$$U=\sqrt{2gh}=\sqrt{2(9.8)(50)}=31.3\frac{m}{s}<u$$

Thus, the ghost and the calf will make it over the hill that is 50.0 m high.