Suppose you are helping Galileo measure the acceleration due to gravity by dropp

Question

Suppose you are helping Galileo measure the acceleration due to gravity by dropping a canon ball from  the tower of Pisa. You measure the height of the tower to be h=183 ft, and you estimate that the uncertainty is .2ft. you measure the drop time using your pulse and arrive at t= 3.5 secwith an estimated uncertainty t= .5 sec.  Youperform the experiment just one time. if the formula for the propagated error is       (rac{partial g}{ g} = sqrt{(rac{partial h}{ h})^{2} + (2rac{partial t}{2})^{?}})

what would you report as your result ( including uncertainty) in ft/sec squared? Find gexp and delta g.

Explanation / Answer

so y = 1/2 a t^2

g = 2 h/t^2 = 2*183/3.5^2=29.88 ft/sec^2

delta g = 29.88*sqrt( (.2/183)^2 +(2*0.5/3.5)^2) = 8.5

so you would report

30 +/- 9 ft/sec^2

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