In a test of air drag, a sphere is launched at various speeds (x, in m/s) and the resulting drag force (y, in N) is determined. The force measurements have an accuracy of 5%.

Lord Rayleigh asserted that there is a power-law relationship between x and y, with exponent near 2.

1. Fit this data to a power law relationship.
2. Consider Rayleigh's scientific claim of an power law. Does this evidence (data) confirm or contradict this claim? Support your answer quantitatively.
3. Properly report (sigfigs, error, units) the exponent for the best-fit power law.

F = C_D (0.5 ρ π R²) v²

where C_D is the drag coefficient and the quantity in parentheses has the value:

(0.5 ρ π R²) = 0.03 kg/m

So:

C_D = A / (0.03 kg/m)

Do an additional fit with the exponent held fixed at 2.

4. Properly report (sigfigs, error, units) the A parameter for this second fit.
5. Use a spreadsheet to calculate the drag coefficient from A, and properly report (sigfigs, error, units) the value.
6. Self-document the spreadsheet and turn in a hardcopy of the page.
7. Make a hardcopy plot of the data with best-fit curve. Make an additional hardcopy plot with scales chosen so as to linearize the curve.
8. Turn in fit reports from both fits (i.e., steps 3 and 4).

X (m/s)	Y (N)
1.53	3.13E-2
2.4	7.67E-2
2.9	0.107
5.2	0.401
5.5	0.411
12.7	2.17
22	6.19
27	9.81
49	28.8
79	82.6