You and your friend Peter are putting new shingles on a roof pitched at 20°. You're sitting on the very top of the roof when Peter, who is on the edge of the roof, 5.5 m away, asks you for the box of nails. Rather than carry the 2.5 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 0.54, with what speed should you push the box to have it gently come to rest right at the edge of the roof?

Step-by-step explanation:

From conservation of energy, net work done on the box is equal to the change in kinetic energy of the box. This is written mathematically as:

1/2mvf^2 - 1/2mv^2 = mgdsintheta + (-umgdcostheta)

Where Vf= final velocity of box

V = initial velocity of box

d= distance travelled by the box

U= coefficient of kinetic friction

Theta= angle between the edge of the roof and the ground

-1/2(2.5)V^2= (2.5×9.8×5.5×Sin20° ) + (-(0.54)×9.8× 5.5× cos20°)

-1.25V^2= 46.09 + (-68.38)

-1.25 V^2 = -22.29

V^2 = -22.29/-1.25

V^2 = 17.83

V = Sqrt(17.83)

V = 4.22m/s