?

Free Version
Difficult

# Spring Launched Roller Coaster

SATPHY-9XMNVF

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.

A

$32x$

B

$16x$

C

$8x$

D

$4x$

E

$2x$