You and your friend Peter are putting new shingles on a roof pitched at 21? . Yo

Question

You and your friend Peter are putting new shingles on a roof pitched at 21? . You're sitting on the very top of the roof when Peter, who is at the edge of the roof directly below you, 5.4m away, asks you for the box of nails. Rather than carry the 2.5kgbox 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 0.53, with what speed should you push the box to have it gently come to rest right at the edge of the roof?

Explanation / Answer

Forces :
mgsin theta - mumgcos theta = ma

g*sin theta - mu*g*cos theta = a

9.8*sin 21 - 0.53*9.8*cos 21 = a

a = -1.337 m/s^2

so you have final velo = 0 m/s

initial velo = ? m/s

Given d = 5.4 m

u can get it by kinematics
vf^2 = vo^2 + 2ad

0 = vo^2 + 2*-1.337*5.4

vo = 3.8 m/s --> Answer

Answer: 3.8 m/s

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