You are a member of an alpine rescue team and must project a box of supplies, with mass m, up an incline of constant slope angle α 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, with kinetic friction coefficient μk.

Question

You are a member of an alpine rescue team and must project a box of supplies, with mass m, up an incline of constant slope angle α 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, with kinetic friction coefficient μk.
Part A
Use the work-energy theorem to calculate the minimum speed v that you must give the box at the bottom of the incline so that it will reach the skier.
Express your answer in terms of some or all of the variables m, g, h, μk, and α.

Elena · Answer

KE=PE+W(fr) KE=mv²/2 PE= mgh W(fr) =F(fr) •s=µmgcosα•h/sinα mv²/2 =mgh+µmgcosα•h/sinα Solve for ‘v’