A truck with mass m has a brake failure while going down an icy mountain road of constant downward slope angle ?. Initially the truck is moving downhill at speed v₀. After careening downhill a distance L with negligible friction, the truck driver steers the runaway vehicle onto a runaway truck ramp of constant upward slope angle ?. The truck ramp has a soft sand surface for which the coefficient of rolling friction is ?_r.

What is the distance that the truck moves up the ramp before coming to a halt? Solve using energy methods.

Express your answer in terms of m, ?, v₀, L, g, ?, and ?_r.