Pictured below is an amusement park ride where riders are launched in a roller coaster car by a spring to send them over a hill that is $310\ ft$. above the starting level (as pictured below).
If compressing the spring a distance $x$ causes the roller coaster to go up to a height of $20\ ft$. above the starting level, which of the following amounts is the least compression that will allow the coaster to make it over the $310\ ft$. hill?
Assume that conversion of energy to thermal energy is negligible.