A projectile is fired with muzzle velocity v uphill over ground that slopes at an angle α to the horizontal. If the angle of projection is θ to the horizontal:

Question

i) show that the horizontal range is x = 2v2 (cos θ sin θ − cos2 θ tan α) /g

ii) find the direction of aim θ to achieve maximum range. To gain maximum marks,
you should write the solution θ as a linear function of α.