You are working for a physicist in the lab, and she asks you to look over some d

Question

You are working for a physicist in the lab, and she asks you to look over some data for her. She is measuring the acceleration of a falling body using photogates and expects the data to fit a polynomial where:

y = y0 + v0*t - 1/2 *g *t^2 (the general equation for falling bodies).

She gives you her data table

time t

x

height

y

Use the equation and the method of least squares to find the best estimate for the three coefficients. Use this information to now find the best value of g, and compare to the actual known value of gravity. How good is this fit?

Identify the type of problem and statistics to be used and justify/explain your answer.

time t

x

0.2 0.3 0.4 0.5 0.6

height

y

131 113 89 51 7

Explanation / Answer

answer

y0=136.2, v0=67.1429, and , g=942.8572

folowing information is generated using regression analysis for y = y0 + a*t +b*t^2

here intercept=y0=136.2

a=67.1429=vo

b=-471.4286=-g/2

or, g=471.4286*2=942.8572

Analysis of Variance Source DF Sum of
Squares Mean
Square F Value Pr > F Model 2 9921.14286 4960.57143 2712.81 0.0004 Error 2 3.65714 1.82857 Corrected Total 4 9924.80000

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