ees. If accuracy is not a consideration however, it is possible to round 6 pi up to 20, since 6 pi is actually 18.85… The next equation we found was with the physics of aerial shell fireworks. There was a chart listing all the commonly used shell sizes and their corresponding initial mortar velocities. (we will enclose the chart as a reference on the back. ) The relationships between the initial velocities and the distances traveled by the shells may be found using this formula: Vertical height= Initial vertical velocity * Hang time + 0.5 * Acceleration due to gravity* Hang time ^ 2. However, in light of the constraints placed upon us, we have designed our own experiment. Since fireworks are out of season and illegal at this time, we have decided on using bottle rockets, the most harmless and easily accessible variety.Proposed experimentWith our knowledge of arcs and trigonometry, we can calculate the height of a firework based on the distance traveled and the angle at which it is fired. Once we have that information, we can figure out the initial velocity of a firework based on its angle of trajectory.Given the distance traveled of a firework (we’ll call that distance d) we can find the apex of the firework’s trajectory. The apex is always half the total distance traveled (we’ll call that x which is equal to d/2). Based on the degree of the angle of trajectory as well as the horizontal distance traveled to apex, we can determine the height that the firework reaches at its peak. We know from Trig that the tangent of an angle (we’ll be using the tragectory angles of 30, 45 and 60 degrees) is height over distance traveled. (Tangent of theta= x divided by y (height of firework at its peak) Thus, with that information at our disposal, we are able to plug the height back into the following equation:Vertical height = Initial vertical velocity * Hang time + 0.5 * Acceleration due to gravity (9.8m/s)* ...
