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 friction in the gravel brings the truck safely to a halt.

Question

Suppose a gravel ramp slopes upward at 4.70° and the coefficient of friction is 0.410. Find the length of a ramp that will stop a 14980.0 kg truck that enters the ramp at 37.0 m/s.

Answer 1

The gravel will work efficiently if the brakes of the truck are at least working, even though they may not be in perfect condition.

The kinetic energy, Ek of the truck on entering the ramp
=(1/2)mv²

Increase in potential energy, Ep, at the end of the ramp of length L
=mgLsin(θ)

Work done, W, against friction
=μmgcos(θ)*L

Equate energies and work done:
Ek=Ep+W
and solve for L.
I get L=142 m. approximately.
Check my work.