A block of unknown mass is sent up an incline plane of 30 degrees with an initial velocity of 3 m/s. The coefficient of friction is 0.5. Find the distance the block travels up the incline before it stops.
F = ma
v^2 = (v_0)^2 + 2a(x - x_0)
The Attempt at a Solution
So the vertical forces of the incline are the normal force which is equal to mgcos(30). Therefore, the force of friction is (0.5)*mgcos(30).
So taking going up the incline to be positive, we have mgsin(30) - (0.5)*mgcos(30) = ma. We can cancel out the masses. So then we have acceleration = ((2-sqrt(3))(9.8)/4. This turns out to be positive, but it should be negative because the friction should overcome gravity eventually (maybe not, but this problem is implying it). What did I do wrong so far?