# Determining An Appropriate Parabolic Model Report

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Determining an Appropriate Parabolic Model

In this procedure, I am trying to determine an appropriate parabolic model that fits the data I collected of whirlybird wing length vs. time, doing so by using first principles. Also to find out which wing length would produce longest flight time.

Method:

Firstly, I made a whirlybird model and timed how long it took to reach the floor from a certain height. This procedure was repeated several times, each time lessening the wing length and keeping the same height. For each wing length, the bird was dropped three times for maximum accuracy. Once this data was collected it was transferred into a graph, and strange points were excluded. After this an appropriate …show more content…

As a gets closer to 0 the parabola becomes wider. The result was still too thin.

The next function was:

Y= -0.05(X-8)2+2.33

I changed -0.1 to -0.05. As a gets closer to 0 the parabola becomes wider. The result was still too thin.

The next function was:

Y= -0.03(X-8)2+2.33

I changed -0.05 to -0.03. As a gets closer to 0 the parabola becomes wider. The result was off centre to the left.

The next function was:

Y= -0.03(X-8.5)2+2.33

I changed -8 to -8.5. As b decreases the turning point moves to the right. The result was a little too wide.

The next function was:

Y= -0.035(X-8.5)2+2.33

I changed -0.03 to -0.035. As a gets farther from 0 the parabola becomes thinner. The result was a little too thin.

My final function was:

Y= -0.033(X-8.5)2+2.33

I changed -0.035 to 0.033. As a gets closer to 0 the parabola becomes wider.

Below the final quadratic function, Y= -0.033(X-8.5)2+2.33 is superimposed onto my original data points.

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In the tables below, the results when the different lengths are substituted into the function, can be compared with our initial