A block is placed on a plane inclined at an angle θ. The coefficient of friction between the block and the plane is µ = tan θ. The block is given a kick so that it initially moves with speed V horizontally along the plane (that is, in the direction perpendicular to the direction pointing straight down the plane). What is the speed of the block after a very long time?
The Attempt at a Solution
The force of friction exactly balances the gravitational force along the incline. So there will be no acceleration along the inclined plane and the trajectory of the block must be a straight line and it continues to move in its original direction of motion. The frictional force will act opposite to its velocity and after a long time the block should stop. So the final velocity should be 0. But this is not the correct answer. I can't figure out what's wrong with my reasoning.