When races are timed manually, timers start their watches when they see the smoke from the starting gun rather than when they hear the gun. How much error is introduced in timing a 100-m race if the watch is started on the sound rather than on the smoke
t = 100m / 343m/s = 0.292 s.
To calculate the error introduced in timing a 100-meter race if the watch is started on the sound instead of the smoke, we need to consider the speed of sound and the speed of light.
When a race is timed manually, the human timer may start their watch either on the sound of the starting gun or on the smoke from the gun. The reason for starting the watch on the smoke is because light travels faster than sound.
The speed of sound in air is approximately 343 meters per second, or 343 meters/second. On the other hand, the speed of light is approximately 299,792,458 meters per second, or 299,792,458 meters/second.
In a 100-meter race, starting the watch on the sound instead of the smoke introduces a delay equal to the time it takes for sound to travel 100 meters.
To calculate this delay, we can use the equation:
Delay = Distance / Speed
Delay = 100 meters / 343 meters/second
Simplifying,
Delay = 0.291 seconds (rounded to 3 decimal places)
Therefore, starting the watch on the sound instead of the smoke introduces an error of approximately 0.291 seconds in timing a 100-meter race.
Keep in mind that this is a simplified calculation and there may be additional factors that can affect the accuracy of the timing. For professional races, electronic timing systems are typically used to minimize timing errors.