A block with initial velocity of 10 m/s is sent up an incline at 30 degrees from the horizontal. The coefficient of friction is 0.2x where x is the displacement. Find the maximum distance the block moves up the incline.
F = ma
The Attempt at a Solution
I decided to try and use energy for this one.
Initial energy is (1/2)m(10)^2 + friction and final is mgh because the block comes to rest eventually.
So: (1/2)m(10)^2 + friction = mgh
Friction = coefficient * Normal force, so Friction = 0.2x * mgcos(30). Therefore:
(1/2)m(10)^2 + (0.2x*mgcos(30)) = mgh
Masses cancel out:
50 + (0.2x*gcos(30)) = gh
We want to find x because x is along the incline, and sin(30) = h / x, so h = xsin(30) and substitute back in:
50 + (0.2x*gcos(30)) = g(xsin30)
50 + 1.697x = 4.9x
50 = 3.203x
x = 15.6 meters
The solution is 5.31 meters, though. What have I done incorrectly?