Physics ch 5 homework help please?

Question

You are a member of an alpine rescue team and must get a box of supplies, with mass 3.00 kg, up an incline of constant slope angle 30.0degrees so that it reaches a stranded skier who is a vertical distance 3.40 m above the bottom of the incline. There is some friction present; the kinetic coefficient of friction is 6.00×10−2. 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/s^2.

Q - 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.

Answer 1

first make a free body diagram

mgsinx+fmgcosx=ma--------------------1...

where x=30 degrees and f=kinetic friction

N=mgcosx

now put values in the first eqn. and u will get acceleration

now mgh=1/2 mv^2=ma* distance

where distance =3.40sinx

put the values and find the answer