Solving Work & Forces Problems: Alpine Rescue Team

[deuce123]

Homework Statement

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.

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.

Homework Equations

Work=1/2(mv^2)-1/2(mv^2)--------- the negative velocity being the initial.
Work=Fd[/B]

The Attempt at a Solution

I got the correct solution through checking online because of the system telling me I did my trig. wrong. I need clarification as too why the answer was what it is. In the answer They use cos of the angle for the friction force, but when I break up the components, the x component of gravity is sin, so I don't understand how they got cosine.

 

[Chestermiller]

Homework Statement

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.

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.

Homework Equations

Work=1/2(mv^2)-1/2(mv^2)--------- the negative velocity being the initial.
Work=Fd[/B]

The Attempt at a Solution

I got the correct solution through checking online because of the system telling me I did my trig. wrong. I need clarification as too why the answer was what it is. In the answer They use cos of the angle for the friction force, but when I break up the components, the x component of gravity is sin, so I don't understand how they got cosine.

Please show us the details of what you did, including free body diagram.