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Kinematic Analysis of a Balloon's Flight Path and Interaction with a Diver

An analysis of the flight path of a balloon, incorporating principles of kinematics and its interaction with a diver.

Caleb Patterson
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Kinematic Analysis of a Balloon's Flight Path and Interaction with a DiverSolution: This is the simple example of kinetic equations𝑑=π‘’βˆ—π‘‘+12π‘Žπ‘‘2Here d= distance covered in time t from the starting pointu is the initial velocity = 0,a is acceleration =g and t is the time= xso𝑑=12𝑔π‘₯2Butthis is distance from the launching padsoDistance from ground =h(x) = 15-dβ„Ž(π‘₯)=15βˆ’12𝑔π‘₯2when h(x) = 0 , Leita’s feet touches waterso time =π‘₯=(15βˆ—2𝑔)12=3.0612=1.75𝑠𝑒𝑐

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Solution:The parameters are(π‘₯(𝑑),𝑦(𝑑))π‘€β„Žπ‘’π‘Ÿπ‘’,𝑦(𝑑)=12𝑔𝑑2π‘Žπ‘›π‘‘π‘₯(𝑑)=𝑑The equations is𝑦(𝑑)=15βˆ’12𝑔[π‘₯(𝑑)]2,Solution: Now the origin is shifted at 50ft away from the origin coordinate system whoseparameters were𝑦(𝑑)=12𝑔𝑑2π‘Žπ‘›π‘‘π‘₯(𝑑)=𝑑Now due to shift in coordinate systemthe parameters(π‘₯(𝑑),𝑦(𝑑))areπ‘₯(𝑑)=π‘‘βˆ’50,𝑦(𝑑)=15βˆ’12𝑔(π‘‘βˆ’50)2Tmin= 0, Tmax=51.75, Tstep= .01Window:[Xmin,Xmax,Xscl]*[Ymin, Ymax, Yscl]=[-50, 1.75, 49.99]*[-12235, 6.42,-12230.10]Solution:5.9ftMaximum height achievedHA15015ft6ft
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Physics

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