Truck brakes can fail if they get too hot. In some mountainous areas, ramps of loose gravel are constructed to stop runaway trucks that have lost their brakes. The combination of a slight upward slope and a large coefficient of rolling friction as the truck tires sink into the gravel brings the truck safely to a halt. Suppose a gravel ramp slopes upward at 6.0 degrees and the coefficient of rolling friction is 0.40.
Use work and energy to find the length of a ramp that will stop a 15,000 kg truck that enters the ramp at 35 m/s.
W= ΔKE + ΔU
The Attempt at a Solution
W = KEf-KEi +Uf-Ui
Given Ui = 0 and KEf = 0,
W = -KEi + Uf
F⋅d = 1/2mVi^2 + mghf
F= mgsin(Θ) + μmgcos(Θ)
(mgsin(Θ) + μmgcos(Θ))d = 1/2mVi^2 + mghf
This is where I get stuck. In the end, I am left with two variables hf and d. I can't actually solve for one variable without the other. Where did I go wrong?