You have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up a 13-m-high hill, then descends 20 m to the track's lowest point. You've determined that the spring can be compressed a maximum of 2.3 m and that a loaded car will have a maximum mass of 420 kg. For safety reasons, the spring constant should be 10 % larger than the minimum needed for the car to just make it over the top.

a) What spring constant should you specify? Express your answer with the appropriate units.

b) What is the maximum speed of a 360 kg car if the spring is compressed the full amount? Express your answer with the appropriate units.