Finding the speed with kinetic friction

[dominatesean]

Homework Statement

You and your friend Peter are putting new shingles on a roof pitched at 20degrees . 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 2.1 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 0.51, with what speed should you push the box to have it gently come to rest right at the edge of the roof?

Homework Equations

normal force up y-axis
mg down y-axis
angle left of -y
friction positive x
not 100% sure if these are right

n-mg*cos O=may
fk+mg(sin O)=max
vf=vi+at
xf=xi+vi*t+.5at^2

The Attempt at a Solution

first get normal force which solve for 1st equ.
n=2.1(9.8)cos20=19.34
then find kinetic friction
19.34*.51=9.86
put into next equation
9.86+2.1(9.8)sin20=2.1*a
a=8.047

plug into kinematic equ.
5.4=0+0*t+.5(8.047)t^2
t=1.15
vf=8.047*1.15
vf=9.3

obviously not right cause I am not sure about the free-body diagram any help would be fantastic.

 

[LowlyPion]

What will the acceleration (deceleration) be?

It will be the gravity component down the slope less the frictional slowing = g*sinθ - μ*g*cosθ = a

Since the final velocity is 0, now you can simply use the V² = 2*a*x

 

[dominatesean]

thank you my friend...that was much easier then I thought it was.