Question

Time (s) Velocity (mph) The velocity change respect to time of a free fall is given left. Accordingly, calculate the velocity value at 5.5 s 0 0 1 22 a) using the $2^{nd}$ order Lagrangian interpolation polynomial (determine the appropriate points to be selected yourself). 2 42 3 60 4 75 b) Obtain the $2^{nd}$ order polynomial equation suitable for these data by using the least squares method and calculate the velocity value at 5.5 s using this equation. c) Determine the quality (determination coefficient) of the polynomial obtained in part b using the $R^2$ method. 5 87 6 96 7 103 8 108 9 111 10 114

          Time (s)
Velocity (mph)
The velocity change respect to time of a free fall is given left.
Accordingly, calculate the velocity value at 5.5 s
0
0
1
22
a) using the $2^{nd}$ order Lagrangian interpolation polynomial (determine
the appropriate points to be selected yourself).
2
42
3
60
4
75
b) Obtain the $2^{nd}$ order polynomial equation suitable for these data by
using the least squares method and calculate the velocity value at 5.5
s using this equation.
c) Determine the quality (determination coefficient) of the polynomial
obtained in part b using the $R^2$ method.
5
87
6
96
7
103
8
108
9
111
10
114

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time s velocity mph the velocity change respect to time of a free fall is given left accordingly calculate the velocity value at 55 s 0 0 1 22 a using the 2nd order lagrangian interpolation 61361

Added by Colin P.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Ivan Kochetkov

12/04/2024

Step 1

Since we want to calculate the velocity at $t = 5.5$ s, we should choose points that are close to $t = 5.5$ s. A good choice would be $t=5$, $t=6$, and $t=7$. The data points are: $(t_0, V_0) = (5, 87)$ $(t_1, V_1) = (6, 96)$ $(t_2, V_2) = (7, 103)$ The Show more…

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Time (s) Velocity (mph) The velocity change respect to time of a free fall is given left. Accordingly, calculate the velocity value at 5.5 s 0 0 1 22 a) using the $2^{nd}$ order Lagrangian interpolation polynomial (determine the appropriate points to be selected yourself). 2 42 3 60 4 75 b) Obtain the $2^{nd}$ order polynomial equation suitable for these data by using the least squares method and calculate the velocity value at 5.5 s using this equation. c) Determine the quality (determination coefficient) of the polynomial obtained in part b using the $R^2$ method. 5 87 6 96 7 103 8 108 9 111 10 114

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