Hooke’s law problem

1. The problem statement, all variables and given/known data

You have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up a 10-m-high hill, then descends 20m to the track’s lowest point. You’ve determined that the spring can be compressed a maximum of 2.5m and that a loaded car will have a maximum mass of 450kg . For safety reasons, the spring constant should be 12% 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 370kg car if the spring is compressed the full amount?

2. Relevant equations

(1/2) kx^2 = mgh
(1/2)kx^2 = (1/2) mv^2

3. The attempt at a solution

I solved the first question which was 1.6*10^4 (rounded to two sig figs) and the system accepted it.. but it won’t accept my answer for the second one, please see if I really have anything wrong:

(1/2)kx^2 = (1/2) mv^2

v = sqrt(kx^2/m)

v = sqrt(1.6*10^4 N/m * (2.5 m)^2 / 450 kg)

v = 14.8 m/s

To two sig figs = 15 m/s.. which it says is wrong..



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