Different launch angles for a tennis ball

How far can you throw a tennis ball? Our goal is to find the launch angle θ, measured up from the ground, that will result in the ball traveling as far forward (in the x direction) as possible. Assume that you can throw the ball at 12 meters/second from a height of 2 meters.

When you need to account for drag, you can assume that the ball’s radius is 0.0265 meters, the ball’s mass is 0.058 kg, the drag coefficient is 0.5, and the density of air is 1.21 kg/meter

We were told to use eulerballistic function

function z = eulerballistic(f, z0, deltat)
z = z0;
i = 1;
while z(2,i) > 0

   zprime = f(z(5,i), z(:,i));
   z(:,i+1) = z(:,i) + deltat*zprime;

   i = i + 1;
   if i > 100
       break;

end end
end

With everything going on, I have forgotten some of how to start a problem like this. Any help would be much appreciated.

[darova]

I think you need 2 component of velocity

- horizontal velocity (drag only)

- vertical velocity (drag and gravitation)

[James Tursa]

I'm assuming the density is 1.21 kg/meter^3, not 1.21 kg/meter.

[James Tursa]

How is z defined? (i.e., what are each of the elements?). How is f defined?