You are the finest roller coaster designer in the world, and you come up with the idea of having a roller coaster travel at a top speed of 200 km/h.

a .Neglecting air resistance and if it starts at rest at the top, how high do you have to make the first hill to achieve the desired speed(of 200 km/h) at the bottom?

b. Now that you have your coaster traveling at such high speeds after the first hill, you decide to make a giant loop. You want to ensure that the train is traveling at least 50km/h at the top of the loop. How tall can you make you make the loop?

c. At the end of the track there is a station for people to get on and off the train. This station is 10 m off the ground. How fast will the train be going when it enters the station?

d. Now assume that the mass of the coaster is 3000 kg. Once the train enters the station (a 250 m covered length of track), its brakes lock and it slides to rest. How much work must be done for the train to come to a stop?

e. Still assuming that the mass of the coaster is 3000 kg, what minimum braking force must be applied to ensure the train stops by the time it reaches the end of the station?