A person, mass m = 20 kg, sits on a sled on a snowy slope. Assume that the sled is massless. The slope makes an angle = 30degrees to the horizontal. Assume no friction between the sled and the slope. Also assume the person is holding on tightly to the sled so they are not going to come off of it. In order to stop them from sliding down the slope, I push on them. But I don't push directly up the slope, instead I push exactly horizontally (the x direction) into the slope.

(a) Draw a free body diagram for the person and their sled. Make sure to include all forces acting on this system.

(b) Can I possibly hold them steady by doing this, and if so what force would I need to apply?

(c) Assume that the length of the slope is d = 100 m and we are sitting a distance of 20 m from the bottom of the slope. If at t = 0 I start exerting a force of 120 N (in the same direction as above), what is the distance of the sled from the top of the slope as a function of time? Make a plot of the function you found.