1. The problem statement, all variables and given/known data A sled goes down a frictionless hill onto flat ground with friction. The sled comes to a stop in some distance. The height of the hill, the angle of the hill w.r.t the horizontal, the initial velocity of the sled, and the coefficient of kinetic friction are all known. I want to solve this without using conservation of energy. 2. Relevant equations Constant acceleration equations of motion, Newton's 2nd law. 3. The attempt at a solution The velocity at the bottom of the hill can be found using the appropriate kinematics equation. This velocity can then be used as the initial velocity in solving how far the sled travels on the flat ground. My question is regarding the velocity at the cusp point between hill and flat ground. What is a good argument for why the entire final velocity on the hill should be used for the initial velocity on the flat (as opposed the horizontal component)? If I draw a free body diagram at the cusp point, I want the forces to net to zero in the direction perpendicular to half the hill angle in order for direction, but not magnitude of velocity to change. When I do this, I get an expression that's not clear to me why it equals zero: W*sin(Θ/2)-μk*N2*cos(Θ/2)+N1sin(Θ/2)-N2sin(Θ/2)=0 where W=weight of sled, Θ=hill angle, μk=coefficient of kinetic friction, N2=normal force of flat on sled, N1=normal force of hill on sled. The values of N1 and N2 at the cusp point seem like they should be different than when the sled is either only on the hill or only on the flat. I want to understand this without invoking conservation of energy.