A matchbox car (mass = 8.3 kg) is left on a hill which is at an angle of 22 degrees. The toy car is at rest on the x axis. The coefficient of kinetic friction between the toy and the ground is 0.33, while the coefficient of static friction is 0.37.

a) Draw the free body diagram for the matchbox toy.

b) Solve for the friction force.

If a parent comes along and starts pushing the toy car parallel to the direction of the hill (up the hill) with a 50 Newton force.

c) What is the acceleration of the car up the hill once the parent gets the toy car moving?

d) If the parent pushes it with the same constant force for 3 minutes starting from rest, how far does the toy car travel up the hill?

e) How much work is done by friction?

f) What is the change in gravitational Potential energy?