An alpine rescue team member must propel a box of supplies, with mass m, up an incline that makes an angle theta with the horizontal so that it reaches a stranded skier who is a vertical distance h above the bottom of the incline. The incline is slippery, but there is some friction present; the kinetic friction coefficient is mu_k.
Use the work-energy theorem to calculate the minimum speed, , that the member must impart to the box at the bottom of the incline so that it will reach the skier.