A roller$-$coaster car rolls down a track, reaching a speed of v$0$ at the bottom. If the height of the track is increased by a factor of $2\mathrm{.}00,$ assuming the track is frictionless, by what factor will the speed at the bottom increase?

$2\mathrm{.}00$

$4\mathrm{.}00$

$1\mathrm{.}41$

$3\mathrm{.}00$