What speed should you push the box

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SUMMARY

The discussion revolves around calculating the speed required to push a 2.3 kg box of nails down a roof pitched at 23 degrees, ensuring it comes to rest at the edge, 5.4 m away. The coefficient of kinetic friction is 0.50. The solution involves applying the work-energy principle, where the work done against friction equals the change in kinetic energy. The participants emphasize using energy concepts to solve the problem, specifically focusing on the relationship between initial kinetic energy and the work done by friction.

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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
 
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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
 

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