- #1

cmkluza

- 118

- 1

## Homework Statement

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

## Homework Equations

To find time I used the following equation:

[tex]t=\sqrt{\frac{2(\frac{D}{100})}{9.81}}[/tex]

D is measured in cm, hence the division by 100 (to get meters).

9.81 is acceleration due to gravity (this comes from [itex] x = \frac{1}{2}at^2[/itex])

While measuring D, I used a measuring stick with smallest unit 1cm. Therefor, uncertainty of D is [itex]\pm[/itex]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: [itex]\pm 0.05cm \longrightarrow \frac{0.05}{15.48} \times 100 = \pm 0.32[/itex]%.

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: [itex]\frac{1}{2} \times 0.32 = \pm 0.16[/itex]%.

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.