Puck A is launched by a spring initially compressed through a distance $x$ across a level, frictionless sheet of ice. After reaching the edge of the ice sheet, it continues sliding across level pavement through a distance $d$ until slowing to a stop. Through what distance would the spring need to be compressed in order to get an identical puck B to slide $3$ times as far across the pavement? $($Answer: $\sqrt[\phantom{2}]{3}x$ or $1\mathrm{.}73x)$