the following problem is from the 5th edition of Thorton and Marion's "Classical Dynamics" ch.2 problem 14 p.92 The problem statement, all variables and given/known data A projectile is fired with initial speed v_0 at an elevation angle of alpha up a hill of slope beta (alpha > beta). (a) how far up the hill will the projectile land? (b) at what angle alpha will the range be a maximum? (c) what is the maximum angle? The attempt at a solution apparently this has been a stumper in former classical mechanics classes, but here was as far as i got: i broke down the components of the forces into x and y x-component: a_x=0 integrating --> v_x = v_0 cos(beta) integrating --> x = v_0 t cos(beta) a_y = -g integrating --> v_y = -gt + v_0 sin (alpha - beta) integrating --> y = ( -gt^2 / 2 ) + v_0 sin (alpha - beta) the answer in the back of the book for part (a) is: d = (2 v_0^2 cos(alpha) sin(alpha-beta) ) / (g cos^2(beta)) any idea how to get from the components to the answer?