You and your friend Sam are putting new shingles on a roof pitched at 21 degree. You are sitting on the very top of the roof when Sam, who is at the edge of the roof directly below you, 5.2 meter away, asks you for the box of nails. Rather than carry the 2.5 kilogram box of nails down to Sam, you decide to give the box a push and have it slide down to him.
If the coefficient of kinetic friction between the roof and the box is 0.51, determine with what speed should you push the box to have it gently come to rest right at the edge of the roof?