A 100-slug projectile is launched from x = 0 y= 0 with initial velocity Vx = Vy =400 ft/s (y axis positive upward). The aerodynamic drag force is of magnitude C|v|^2 where C is a constant.

a.) Derive the equations of motion for the projectile found in example problem 3.9 (pg 148)

b.) Use MATLAB ode45 to plot the trajectories x vs y for C = 0, 0.003, 0.006

c.) Compare the zero crossing of C = 0 to the analytic solution. (use solution to 2.74)

d.) How much further does the projectile go for C = 0 compared to C = 0.006.  Why does the projectile not go as far?  Is 45 degrees still optimal for a given velocity?  What procedure would you use to find the optimal trajectory?

Note: be sure to include your code when handing in your computer assignment.  Also in the notes you recieved in class, anywhere it says "axes" it should say "axis".