1. The problem statement, all variables and given/known data A projectile is fired from a cannon at an angle β with the horizontal at a velocity V. The cannon is situated inside a cave. The cannon is situated at a distance X away from the inner most part of the cave. The cave makes an angle α with the horizontal. What is the angle β, in terms of V,α and X, will the cannon have maximum range? Assume no air resistance 2. Relevant equations Kinematics Equations 3. The attempt at a solution I have tried to create a function that has β as a function of V,α and X, however, when i try to equate the maximum height of the projectile to the height of the cave where the projectile is at maximum(I.E (x+0.5range)tan(α))= (0.5range)tanβ), my α is always affected by β. Any help?