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

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Kinematic Analysis of a Balloon's Flight Path and Interaction with a Diver Solution: This is the simple example of kinetic equations 𝑑 = 𝑢 ∗ 𝑡 + 1 2 𝑎 𝑡 2 Here d= distance covered in time t from the starting point u is the initial velocity = 0, a is acceleration = g and t is the time= x so 𝑑 = 1 2 𝑔 𝑥 2 But this is distance from the launching pad so Distance from ground = h(x) = 15 - d ℎ ( 𝑥 ) = 15 − 1 2 𝑔 𝑥 2 when h(x) = 0 , Leita’s feet touches water so time = 𝑥 = ( 15 ∗ 2 𝑔 ) 1 2 = 3 . 06 1 2 = 1 . 75 𝑠𝑒𝑐
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Solution: The parameters are ( 𝑥 ( 𝑡 ) , 𝑦 ( 𝑡 ) ) 𝑤 ℎ 𝑒𝑟𝑒 , 𝑦 ( 𝑡 ) = 1 2 𝑔 𝑡 2 𝑎𝑛𝑑 𝑥 ( 𝑡 ) = 𝑡 The equations is 𝑦 ( 𝑡 ) = 15 − 1 2 𝑔 [ 𝑥 ( 𝑡 ) ] 2 , Solution : Now the origin is shifted at 50 ft away from the origin coordinate system whos e parameters were 𝑦 ( 𝑡 ) = 1 2 𝑔 𝑡 2 𝑎𝑛𝑑 𝑥 ( 𝑡 ) = 𝑡 Now due to shift in coordinate system the parameter s ( 𝑥 ( 𝑡 ) , 𝑦 ( 𝑡 ) ) are 𝑥 ( 𝑡 ) = 𝑡 − 50 , 𝑦 ( 𝑡 ) = 15 − 1 2 𝑔 ( 𝑡 − 50 ) 2 T min = 0, T max = 51.75 , T step = .01 W indow :[ X min , X max , X s cl ]*[ Y min , Y max , Y scl ] =[ - 50, 1.75, 49.99]*[ - 12235, 6.42, - 12230.10] Solution: 5.9ft Maximum height achieved H A 15 0 15 ft 6 ft

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