>>12371398oookaayy, It's been awhile since I was in physics, but I'll try to help you out.
Essentially the problem presented is how much Work it takes to raise a 100kg cart vertically 10m.
We can calculate W = 9.8m/s^2(gravity acceleration) * 100kg(mass of cart) * 10m(distance) = 9800 Joules
The minimum starting speed is the speed at which cart exectly enough KE to climb to top of hill, KE = work = 9800 J
Classical mechanics lets us define work to be = 0.5(mass)(velocity)^2
So if we set 9800 = 0.5 * 100kg * v^2, and solve for v, we get v = 14m/s
pretty sure that's how you solve it