# Math Help - Error Analysis

1. ## Error Analysis

Hello everyone!

Just needed quick help on creating a derived formula for reaction time as a function of distance fallen...

Me and my partner did a reaction lab and I had my partner drop a ruler between my thumb and index finger. I was to stop the ruler as quickly as possible and see the distance the ruler went (in centimeters).

We did this about 40 times (so we have 40 measurements) and we have the average (mean) distance, standard deviation of the distance fallen, 2/3 inclusive individual measurement lower limit and upper limit, deviation of the mean, and finally, the 2/3 inclusive mean lower and upper limits.

Now I'm told to create a derived formula for reaction time as a function of distance fallen... How do I get this? I'm stuck and unfortunately, it's the weekend and I can't talk to my professor >_<

Thank you so much for your time and help!

Sincerely,

2. The formula is $s = \tfrac12gt^2$ (where s is the distance fallen). So the time t is given by $\boxed{t = \sqrt{\frac{2s}g}}$.

It might be more meaningful to find the time for each of the 40 measurements, and then do the error analysis on the times rather than the distances.

3. Thank you Opalg!

Our professor actually wanted us to measure only the distances... I believe he wants us to use the derived formula to find the 't' time.

The final thing I got going here is that I need to figure out the reaction time calculations using the derived formula.

On the chart that I need to fill out, I have to find the Distance Fallen Value (of the first 20 measurements) by inserting Average mean, Mean 2/3 upper limit and lower limit. And I also need to figure out the Reaction Time Value (convert my distances into times using the derived formular?)

How would I get started plugging these in? Do not worry, I will definitely figure out how to do the calculations once I know what I am doing.

Thank you so much for your time,