Hang time ^ 2 … and we will be able to calculate the initial vertical velocity of fireworks fired off at various trajectories. This will enable us to prove the validity of the preceeding equation and allow us to use Trig for a “real world” experiment.HypothesisGiven that a rocket fired from a trajectory of 60 degrees will reach the highest apex, we believe that this rocket will have the highest vertical velocity. This will be the case due to the fact that we think that hang time and acceleration due to gravity will be fairly consistent throughout all trajectories. Therefore, the highest vertical height will yield the highest initial vertical velocity.In proving the trig concept that the tangent of an angle is equal to height over distance traveled, (y/x) we can carry this idea over and find the size of an airborne firework that has exploded. Earlier in this proposal, we explained the equation that one can use in order to determine the size of an exploded firework—that equation is as follows:18.85 (6pi)* time (in seconds) *angle of trajectory =sizeThis equation is essentially the same as our earlier notion that the height of the bottle rocket is equal to the tangent of the angle at which it is fired –(unknown height over distance traveled divided by two.) What makes this slightly different from the height equation is that rather than finding the height of the rocket at its peak, this equation allows you to find the size of the firework once it has exploded (as that takes the place and is substituted as the “height”) There are many variables and trivial differences present between the products of different manufacturers, however few other than the experts will notice them. Pyrotechnics is obviously a risky hobby in which very few people can dabble, unlike most other leisure activities. In this pastime of fireworking, progress is actually the development and creation of new effects. By exper...
