I work for Big Top Circus, and hope that you can help me as a consultant. We have been lucky enough to find a human cannonball that would agree to tour with us for a reasonable fee. This fellow, Bucky, brings his own 15 foot long cannon, and claims that when shot out of the cannon with a muzzle speed of 70 miles per hour, he can fly 150 feet, landing in a well-prepared, large, net. If we hire Bucky, we would like the show to be really spectacular. We’d like to shoot him over our ferris wheel and through a flaming hoop dropped by a crane. The ferris wheel is 60 feet tall and would be 75 feet from the cannon (midway between the cannon and the net – we think that’s probably safest). Our hoop is 8 feet in diameter and the crane we would drop it from is 100 feet tall. We could position the crane so that it could drop the hoop 95 feet from the cannon. Would this be a feasible proposition? We’d like to know before we hire this fellow, as we would hate to spend the money and not put on the caliber of show we hope to achieve.
If it isn’t possible, please explain why not and how we might modify the trick in order to make it safer. We can decide from there whether or not we are willing to hire Bucky. In either case, our insurance company is requiring that we submit proof that our stunt will work using calculus rather than the algebraic formulas that we are sometimes taught in physics. The calculations will have to account for the fact that the cannon is on a 2 foot tall sled and that the height of launch will depend on the angle of elevation. We’ll also need clear information about when to drop the hoop so that Bucky would fly through it without burning himself.
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