Golf Ball Physics Probem

Homework Statement

The greenskeepers of golf courses use a stimpmeter to determine how "fast" their greens are. A stimpmeter is a straight aluminum bar with a V-shaped groove on which a golf ball can roll. It is designed to release the golf ball once the angle of the bar with the ground reaches a value of θ = 20.0°. The golf ball (mass = 1.62 oz = 0.0459 kg) rolls 29.3 in down the bar and then continues to roll along the green for several feet. This distance is called the "reading." The test is done on a level part of the green, and stimpmeter readings between 7 and 12 ft are considered acceptable. For a stimpmeter reading of 11.4 ft, what is the coefficient of friction between the ball and the green? (The ball is rolling and not sliding, as we usually assume when considering friction, but this does not change the result in this case.)

http://s172.photobucket.com/albums/w30/afghanplayr/?action=view&current=golf.gif

The Attempt at a Solution

E = K + U + W(work vs. friction )

E = KE + KEi + PE + PEi + uKmgsine(theta)d
since it is at rest initial kinetic and potential are zero

E = 1/2(mv^2) + mgh + uKmgsine(theta)d

KEf = 1/2(0.0459kg)(3.65m/s)^2 = 0.3057 J
PEf = (0.0459)(9.81)(4.2187m) = 1.899 J

Wf= uK(0.0459)(9.81)(sin20)(3.475m)

uK= 1.54

well this is where i realized i was wrong ANY HELPPPPPPPPP I AM REALLY STUCK