Ball fired from cannon homework

1. Sep 17, 2015

zippyjibby

1. The problem statement, all variables and given/known data
A cannon, when aimed vertically, is observed to ﬁre a ball to a maximum height of L. Another ball is then ﬁred with the same speed, but with the cannon aimed up along an incline of length L, inclined at an angle θ. What should θ be so that the ball travels the largest horizontal distance d by the time it returns to the height of the top of the plane?

2. The attempt at a solution
My attempt is a bit messy, as you can see below, but I tried to find an equation to describe the initial velocity at the base of the ramp, and an equation to describe the velocity as it leaves the ramp. Then I plugged that in to basic projectile motion equations, and got d in terms of constants and θ. I then took the deriviative to find the optimal angle, but I could not figure out the equation. The homework is due Friday (9/18/2015) at 5pm, and I have not been able to figure it out.

2. Sep 17, 2015

Ray Vickson

I, for one, seldom attached photos of rough work, and never those that are sideways. I will look at it if you type it out.