1. The problem statement, all variables and given/known data In Austin, Texas there is a Taco Cannon (modified T-shirt cannon) that will be spreading the joy of taco'ey goodness to festival goers. The only information I have is that it can fire 200 feet (60.96 meters). My physics professor allows us extra credit for applying physics knowledge to the world. I want to solve for the possible area in the sky that the tacos can fill if a cannon is fired 360 degrees. I'll apply a Standard Deviation (SD) of (+/-) 5 meters to the 60.96 meters I'm calculating the velocities needed to achieve that range, 60.96 meters, at 45 degrees and 55 degrees. for 45 degrees -5m SD V(initial)= 23.418 m/s Max Height= 13.99 m Δ distance= 55.96 m time= 3.38 sec for 45 degrees +5m SD V(initial)= 25.424 m/s Max Height= 16.49 m Δ distance= 65.96 m time= 3.67 sec With the SD, I have 2. Relevant equations x=vt y=V(initial)t+(1/2)at^2 3. The attempt at a solution 1st I calculated the area on the ground a taco desiring person would be. Area of big circle minus area of small circle= (1219.2)(pi) meters squared) I want to calculate the 3 dimensional air space that a taco may be in at a given time (revolutions of a solid), so I can warn migrating birds of raining tacos. I'm not sure of how to get the function of the trajectory as it arcs through the air. Other than choosing points and making the curve from those data points, is there an easier way? I'm taking an algebra based physics course and we only are working with x and y coordinate independently.