You are a member of an alpine rescue team and must get a box of supplies, with m

Question

You are a member of an alpine rescue team and must get a box of supplies, with mass 2.80 kg , up an incline of constant slope angle 30.0 so that it reaches a stranded skier who is a vertical distance 2.70 m above the bottom of the incline. There is some friction present; the kinetic coefficient of friction is 6.00×102. Since you can't walk up the incline, you give the box a push that gives it an initial velocity; then the box slides up the incline, slowing down under the forces of friction and gravity. Take acceleration due to gravity to be 9.81 m/s2 .

Part A

Use the work-energy theorem to calculate the minimum speed v that you must give the box at the bottom of the incline so that it will reach the skier.

Express your answer numerically, in meters per second.

I got the answer V=4.87... but it was wrong.

Explanation / Answer

initially have to go vertically 2.70 m up. and for that mass have to travel 2.70/sin30 = 5.4 m along incline.

N = mgcos30

friction = u N = 0.06 x m x 9.81 x cos30 = 0.51m

Work done by gravity + Work done by friction = Change in KE

- mg x 2.70 - 0.51m x 5.4 = 0 - mv^2 /2

v^2 = 58.48

v = 7.65 m/s

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