Joe Bob runs a ski resort with the best ski hills in the area. The only thing he lacks is an awesome tubing hill with a tuber lodge at the top. Joe hires your group to design a hill with a mechanism to pull tubers from the back of the hill up to the top so people can slide down the other side and have lots of fun.

Due to budget cuts, Joe Bob cannot produce enough snow to cover the entire hill. There is a 5 meter segment of dirt at the base of the hill. Keep in mind that in order to stay within safety regulations, the tubes should not go faster than 3 $m/s$ during any part of the lift. Joe needs to know the projected cost of the operation of your mechanism.

Once you are the top of hill, Joe wants the fun to begin. In order to keep up with the competition, the tubing hill needs to be exciting. There is a ramp at the bottom of the hill where the tubers will be launched through the air. A 5m diameter flaming hoop is located 15m from the ramp and 10m off the ground. Ensure the tubers complete this stunt through the hoop safely. Totally rad dude!!