2931 words - 12 pages

IntroductionThe earliest examples of projectile motion on earth would most likely have been boulders ejected from volcanoes. Later on it may have been the throwing of rocks and spears. By the time humans started scientific investigations, cannons and guns would have been commonly used in warfare. Flight and space travel would not have been possible without a complete understanding of projectile behaviour. Today projectiles are used in all areas of sport including ball and racquet games. If gravity is the only force assumed to be acting on the projectile a simple set of theoretical equations can be developed. Unfortunately, nothing in real life is simple, for example Physics. When a NFL ball is thrown by the quarterback at a certain angle and velocity it will travel a certain distance. This distance is affected by gravity and other forces which are being put on the ball in flight. The aim of the investigation was to discover the relationship between the total distance the ball travels from leaving the hand to being caught at the same height and the trajectory of the ball at the start of its flight.AimThe purpose of this investigation is to see at what launch trajectory will you get the best result, By this, the best result would be the maximum distance which the ball can travel in the air when leaving at the maximum velocity of a NFL pass which is 31m/s.TheoryThe effects in which will be studied in this investigation are total distance in which the ball can travel in the air in a fully sealed environment only having the force of gravity pulling on the ball in flight. However with the practical experiment there will be more than one effect on the ball, the effects include friction, air resistance and many others. The techniques in which will be used will include mathematical equations which will give you an extremely accurate answer if the sport were to take place in a fully sealed system. Another technique to be used will be a practical experiment; this experiment will see the use of a ramp apparatus to get a constant velocity with the same forces acting against the ball over a period of time. Similar investigations which have been conducted have also seen similar results in these fields of optimal angle.HypothesisIf the balls launch trajectory was to change when leaving the system, then the distance in which the ball travels would change, common knowledge would state that the optimal angle would be 45˚ for the longest pass, however reality isn't that simple.Hypothesis WorkingUse the symmetry of the parabolic trajectory to double the horizontal (x) distance at the position of maximum height (y). The maximum height occurs when the vertical speed Vy = 0.V0y=V0sinθ As a function of time, t:Vy=V0sinθ−gtWhen Vy=0:(1):V0sinθ=gtNow horizontal displacment:x=V0xt=V0cosθt(2):t=xV0cosθSubstituting formula from (2) in (1):V0sinθ=gxV0cosθx=V20cosθsinθgThe range is twice this distance...

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