# Step-by-Step Solution: Reaction Time from Ruler Drop ## 1. Understand the Problem You catch a dropped ruler after it falls **27 cm**. We are to find your **reaction time** (how long it took you to react and catch it). We'll use the kinematic equation for free fall: \[ d = \frac{1}{2} g t^2 \] Where: - \( d \) = distance fallen (in meters) - \( g \) = acceleration due to gravity (\(\approx 10~\text{m/s}^2\)) - \( t \) = time (reaction time in seconds) --- ## 2. Convert Units Given: - \( d = 27~\text{cm} = .27~\text{m} \) - \( g = 10~\text{m/s}^2 \) --- ## 3. Rearrange Equation for \( t \) \[ d = \frac{1}{2} g t^2 \] Solve for \( t \): \[ t^2 = \frac{2d}{g} \] \[ t = \sqrt{\frac{2d}{g}} \] --- ## 4. Substitute Values \[ t = \sqrt{\frac{2 \times .27}{10}} \] \[ t = \sqrt{\frac{.54}{10}} \] \[ t = \sqrt{.054} \] --- ## 5. Calculate \[ t \approx \sqrt{.054} \approx .232~\text{seconds} \] --- ## 6. Final Answer **Your reaction time is approximately \(\boxed{.23~\text{seconds}}\) (rounded to two decimal places).** --- ## Summary Table | Step | Value | |----------------|-----------------| | Distance, \(d\) | .27 m | | Gravity, \(g\) | 10 m/s\(^2\) | | Calculated \(t\) | .232 s | | Final answer | .23 s | --- **Explanation:** The time is calculated using the distance the ruler falls, the gravitational acceleration, and the kinematic equation for constant acceleration. The result, about .23 seconds, represents your reaction time in this experiment.