You have been hired to design a spring-launched roller coaster that will carry two passengers per vehicle. The vehicle goes up a 13 meter high hill, and then descends 20 meter to the track's lowest point. You have determined that the spring can be compressed a maximum of 2.1 meter and that a loaded vehicle will have a maximum mass of 400 kilogram. For safety reasons, the spring constant should be 12 percent larger than the minimum needed for the vehicle to just make it over the top.
Determine the maximum speed of a 360 kilogram vehicle if the spring is compressed the full amount?