Patricia skateboards up a curved ramp $($quarterpipe$)$ and launches herself into the air. She begins her motion with a

speed of $8\mathrm{.}4$ m$/$s at a total distance of $5\mathrm{.}0$ m away from the launch position. In order to launch herself from the top of the

quarterpipe, Patricia does $380$ J of work. Patricia has a mass of $94$ kg and knows that the average friction force acting on

her as she skates across this particular surface is $22$ N$.$ If the quarterpipe has a height of $0\mathrm{.}3$ m$,$ how far above the

quarterpipe does Patricia reach?