An athlete claimed that his timing for a $100$ m dash should be corrected because the starting signal was given by a gun fired from a point $10$ m away from him and the timekeeper was standing close to the gun. The error due to this could be (in seconds) [Given: speed of sound = $300$ m/s]

### Concept & Logic The measurement error in timing is caused by the physical delay of sound traveling through the air. Since the timekeeper is standing right next to the gun, they start the stopwatch instantly upon firing. The athlete, however, must wait for the sound wave to travel $10$ meters before they hear the signal to start running. ### Step-by-Step Solution * **Given:** Distance between the athlete and the starting gun = $10$ m. Speed of sound = $300$ m/s. * **Calculation:** The time it takes for the sound of the gun to cross the gap and reach the athlete's ears is calculated as $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$. * $\text{Time} = \frac{10}{300} = \frac{1}{30}$ seconds. * Converting the fraction to a decimal gives $\frac{1}{30} \approx 0.0333$ seconds. * Because the timekeeper starts the watch $0.033$ seconds before the athlete even knows to start running, an extra $0.03$ seconds is incorrectly added to the athlete's recorded sprint time. ### Exam Strategy & Shortcut Identify that the error is entirely dependent on the time delay of sound over the $10$m gap. Simply divide the distance by the speed of sound: $\frac{10}{300} \approx 0.033$. Find the closest matching option. ### Common Pitfall Students sometimes overcomplicate the scenario by trying to factor in the athlete's running speed. The question is exclusively about the static delay of the sound signal prior to any movement. ### Final Answer Therefore, the correct answer is **$0.03$**.