Quote:
Originally Posted by ShesTheMan
Yes it is, the options are:
a) 24.2 ± 0.5 m/s
b) 24.25 ± 0.04 m/s
c) 24±1m/s
d) 24.25 ± 0.53 m/s
e) 24.2 ± 0.02 m/s
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Ok, so when you're dealing with uncertainties, and particularly uncertainties of functions, your best bet is to use differentiation.
So for this question, you should know that solving for final velocity (Vf) should yield the equation:
Vf = sqrt(2*a*h) = (2*a*h)^1/2
[this comes from the kinematic equation Vf^2 = Vi^2 + 2*a*h, and your Vi = 0]
Now, to get uncertainties from complex functions, you must solve for the derivative of your equation and multiply it by the uncertainty of your variable (you can find this definition on page 84 of your 1b03 lab manual):
Vf = (2*a*h)^1/2
Vf' = 1/2(2)(2*a*h)^-1/2 (uncertainty of a*h)
Vf' = (2*a*h)^1/2 (uncertainty of a*h)
--> the absolute uncertainty of a*h = ah [(delta a/a) + (delta h/h)]
After plugging in all of the numbers, I get 24.3 +/- 0.5
The only thing I'm unsure about is the constant and whether that plays a factor in the absolute uncertainty of a*h. Other than that, I'm pretty sure this method is correct. Please feel free to correct me if I'm wrong.