The Roller Coaster of Doom
A 500 kg roller coaster car sits at rest at the top of the first hill of the Roller Coaster of Doom waiting to thrill its riders. The first hill is 100 m high. The second hill is 20 m high. The car will then travel through a loop that is 50 m high. The car will come to the end of the track, 20 m off the ground, where it will fly off the track, straight up into the air. After this, the car will strike the ground killing all passengers on board. Answer the following questions based on the above information. Assume that there is no air resistance, no friction between the car and the track, and no energy lost to the environment during this ride unless stated otherwise.
1. Point A is at the top if the first hill. Calculate the gravitational potential energy at the top of the hill.
2. Point B is halfway down the hill. What is the magnitude of the kinetic energy at point B?
3. What is the velocity at point C located at the bottom of the first hill?
4. What is the magnitude of the kinetic energy at point D?
5. How fast is the car going at point E located at the top of the loop?
6. The car speeds off the end of the track. What velocity will it have at the very end of the track?
7. Find the time it takes for the car to reach the top of the trajectory where vf = 0.