3Please show your work to ensure maximum partial credit on the following problems. If no work is shown, you will receive zero credit. Please box your final answers.

3) (10 points) Alice stands on a hill inclined 0 degrees above the horizontal. She kicks a ball of mass m kilograms up the hill. The force her foot exerts on the ball is parallel to the hill and her foot is in contact with the ball for At , seconds during the kick. After leaving Alice's foot, the ball moves up the hill a distance L meters before stopping and heading back down the hill. There is a non-zero friction force of magnitude f newtons acting on the ball the entire time (including during the kick). Please answer the following in terms of the variables given above and use g as the magnitude of free-fall acceleration. (HINT: check units) a) Draw pictures of the situation. Label the important moments in time as follows: =to is moment the kick begins, t=t, is moment the ball leaves Alice's foot, t=t2 is moment ball reaches highest point on hill, t=t; is moment the ball gets back to same location where it left Alice's foot. Include displacements, velocities, and accelerations as labeled arrows. Include their magnitudes if you know them, write a question mark if you do not. b) Draw a complete FBD for the ball at a moment on its way up the hill between the times t , and t2 . c) Use the FBD from part (b) to "fill out" Newton's 2"d Law and solve the for the acceleration of the ball on its way up the hill @ 12x d) Find the velocity of the ball as it left Alice's foot V1x e) Find the acceleration of the ball during the kick dolx f) Draw a complete FBD for the ball at a moment during the kick between the times to and t g) Use the FBD from part (f) to "fill out" Newton's 2"d Law and solve for the magnitude of the kicking force F h) (Extra credit! + 3 points!!) Find an expression for the velocity of the ball when it gets back to where it left Alice's foot. HINT: V 3x # V 1x