How Did I Calculate the Speed to Slide Nails Down a Roof?

[mullets1200]

Homework Statement

Okay, so i am reviewing for an exam next week and I've been looking at my online homework and i ran across this problem and I cannot remember how I solved it:

You and your friend Peter are putting new shingles on a roof pitched at 23 degrees. 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.
f 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?

The answer is 2.7 m/s

I am blanking out and cannot remember how I solved this.

Homework Equations

I believe:
Fr=T-fk
a=Fr/m
V=Sqrt(2*a*Muk(fric. force))

The Attempt at a Solution

 

[berkeman]

Homework Statement

Okay, so i am reviewing for an exam next week and I've been looking at my online homework and i ran across this problem and I cannot remember how I solved it:

You and your friend Peter are putting new shingles on a roof pitched at 23 degrees. 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.
f 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?

The answer is 2.7 m/s

I am blanking out and cannot remember how I solved this.

Homework Equations

I believe:
Fr=T-fk
a=Fr/m
V=Sqrt(2*a*Muk(fric. force))

The Attempt at a Solution

You started by drawing a free body diagram of the box, and applying the kinematic equations of motion. Show us your work as you re-create your original work toward the answer. LOL.