Finalizing the Model

On the previous page, you found values for a and b by looking at a pair of graphs and fitting those curves to data visually. Another, more precise method for finding a and b would be to linearly transform equation 7 (rewrite it in the form y = mx + b), and then have a computer best fit a line to the transformed data. As an extra challenge if you have time, you should review how we found the best fit curve analytically. Using the method described in the optional appendix, we found the best fit for the data to be obtained when a = 20.2013 and b = 0.981, so that we have

Exercise 10: Answer the following questions:

a) At what height is the energy expended minimized, on average?

b) Is your answer consistent with your earlier answers?

c) How confident are you with the answer?