We wish to determine the acceleration due to gravity (g) using the following dat

Question

We wish to determine the acceleration due to gravity (g) using the following data and h = 0.5gt^2.

a) Use the least squares technique to find the best value of g. Assume the error in each h (height)

measurement is 0.01 m and the time is measured exactly.

h (m)   t (s)

0.05     0.1

0.44     0.3

1.23     0.5

2.40     0.7

b) What is the value of the chi-square (?^2) for this problem?

c) How many degrees of freedom are there in this problem? (See Taylor Problem 12.14, part b))

d) Estimate the probability to get a ?^2 per degree of freedom ? what you obtain using parts b) and c).

Explanation / Answer

a) ==> 0.5 g = 4.898 ==> g = 2 * 4.898 = 9.80 m/s2

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