You have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up a 13m-high hill, then descends 19m to the track's lowest point. You've determined that the spring can be compressed a maximum of 2.4 mm and that a loaded car will have a maximum mass of 410kg. For safety reasons, the spring constant should be 11% larger than the minimum needed for the car to just make it over the top.

What spring constant should you specify?

What is the maximum speed of a 360kg car if the spring is compressed the full amount?