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Chapter19

# Chapter19 - Problem 19.11 The following data was collected...

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Problem 19.11 The following data was collected for the distance travelled versus time for a rocket: t, sec. 0 25 50 75 100 125 y, km 0 32 58 78 92 100 Use numerical differentiation to calculate velocity and acceleration at each time. At time t=0, we can calculate the velocity by forward differences v=(32 0)/(25 0)=1.28 km/s. We can also use a three point forward difference equation ( 2 ) 4 ( ) 3 ( ) 58 4 32 3 0 '( ) 1.4 2 50 f x h f x h f x f x h We can also fit a quintic polynomial to the data and take its derivative at zero >> t=[0:25:125] t = 0 25 50 75 100 125 >> y=[0 32 58 78 92 100] y = 0 32 58 78 92 100 >> p=polyfit(t,y,5) Warning: Polynomial is badly conditioned. Add points with distinct X values, reduce the degree of the polynomial, or try centering and scaling as described in HELP POLYFIT. p = 0.0000 0.0000 0.0000 0.0048 1.4000 0.0000 >> format short e >> p p = 3.0478e 022 1.0186e 019 1.2065e 017 4.8000e 003 1.4000e+000 7.2060e 015

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Which means that the data fits very well a quadratic polynomial >> v0=p(5) v0 = 1.4000e+000 We verify that a quadratic polynomial will do
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Chapter19 - Problem 19.11 The following data was collected...

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