A block of mass m is moving along a horizontal frictionless surface with a speed of 5.7 m/s. The block encounters a slope which it travels up. If the slope is 11 degrees and the coefficient of kinetic friction between the block and the incline is 0.26, how far does the block travel up the incline?
fk = uk*Fn
K1 + U1+ Wother = K2 + U2
The Attempt at a Solution
Using a free body diagram I found the normal force, Fn, to be
Fn - mgcos(11) =0
Fn = 2.50119
Then using K1 + U1 + Wother = K2 + U2
1/2*m*v^2 - 2.50119m = 9.8*m*h
I solved for h to find the height that the block travels up the ramp
h = 1.40243 m
Then using SOHCAHTOA I solved for the length of the ramp that the block traveled:
1.40243/sin(11) = 7.34992m
I know the answer should be 3.7 meters but I don't know where I'm going wrong.