Finding uncertainty of a measurement

[cmkluza]

Homework Statement

What is your average reaction time? What is the uncertainty?

Homework Equations

To find time I used the following equation:
$$t=\sqrt{\frac{2(\frac{D}{100})}{9.81}}$$
D is measured in cm, hence the division by 100 (to get meters).
9.81 is acceleration due to gravity (this comes from $x = \frac{1}{2}at^2$)
While measuring D, I used a measuring stick with smallest unit 1cm. Therefor, uncertainty of D is $\pm$0.05cm.
My average time and distance are 15.48cm and 0.17s.

The Attempt at a Solution

I'm not certain what the best way to go about this is. So, the first thing I do is convert the absolute uncertainty to a relative uncertainty: $\pm 0.05cm \longrightarrow \frac{0.05}{15.48} \times 100 = \pm 0.32$%.

With a relative uncertainty, multiplication and division by a constant no longer matter, so far as my understanding goes. So, this simplifies down to a square root with a relative uncertainty. Therefore I just multiply my uncertainty by 0.5: $\frac{1}{2} \times 0.32 = \pm 0.16$%.

Is this the correct answer? Something about this whole process just didn't seem right to me, but I've never been good at uncertainties and whatnot.

 

[DrClaude]

That's not correct. Even though you are using relative uncertainties, the uncertainty on t depends on the absolute value of D. Have a look at http://www.rit.edu/~w-uphysi/uncertainties/Uncertaintiespart2.html