What speed should you push the box

[mullets1200]

Homework Statement

You and your friend Peter are putting new shingles on a roof pitched at 23degree . You're sitting on the very top of the roof when Peter, who is at the edge of the roof directly below you, 5.4 m away, asks you for the box of nails. Rather than carry the 2.3 kg box of nails down to Peter, you decide to give the box a push and have it slide down to him.
If the coefficient of kinetic friction between the box and the roof is 0.50, with what speed should you push the box to have it gently come to rest right at the edge of the roof?

Homework Equations

I don't know lol

The Attempt at a Solution

so I drew the free body diagram but I really don't know where to go from there. I think the problem is i just don't know which equations to use. any help is appreciated

 

[andytuki]

Use energies. It starts out with energy that carries it down the roof and stops at the bottom with zero final energy. There was work down on it to change the energy, frictional work.

W = Delta KE