graph
of
the curves and data points
The yellow circles are the data points. The purple(ish) line is the straight line. The blue-green curve is the parabola. The red curve which intersects every data point is the "curve".
If the path of the projectile was a straight line, a straight line should fit the data best and if the path of the projectile was a parabola, an equation having the basic properties of a parabola would fit the data best.
Using linear regression, the best fits were:
y:horz dist x:vert fall Type graph Equation Corr Coef* straight line: y= 0.47x + 7.39 0.9951 parabola : y= 4.26(x^0.5) [x=(0.235y)^2] 0.9998 curve : y= 3.53(x^0.537) [x=(0.282y)^1.86] 0.9999
*Corr Coef = correlation coefficient : tells how closely the equation reflects the data.
I used linear regression a third time to determine exactly what type if curve would fit the data most closely. This curve is almost a parabola.
From the correlation coefficient and the graph it is obvious that the parabola fits the data much more closely than the straight line.
Experiment
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written by: Sharmaine Jennings email address: vanese@owlnet.rice.edu last revised: April 17, 1995