You can estimate your distance from a lightning storm by watching for a lightning flash and then counting in one-second intervals using the general rule that you are 1 km away for every 3 s you count.

Explain why this rule works.
Estimate the distance from a lightning storm if it takes 8 s (exactly) for the sound of the thunder to reach you after you see a flash of lightning. Assume that the temperature is 21 degrees Celsius. (The speed of light is approx. 2.99 x 10^8 m/s.)

assume light travels at very very high speed so you see the lightning immediately.

Then distance = speed of sound * time
distance in km = (1/3) t
so
speed of sound must be about 1/3 km/sec
or about 333 m/s

8/3 km

12km

12km

The rule that you are 1 km away for every 3 seconds you count after seeing a lightning flash is based on the fact that sound travels at a constant speed through the air. In normal conditions, the speed of sound in dry air at 21 degrees Celsius is approximately 343 meters per second (m/s).

When you see a flash of lightning, the light reaches your eyes almost instantaneously because the speed of light is much faster than the speed of sound. However, since sound travels slower, it takes some time for the sound of the thunder to reach your ears.

Now, when you hear the sound of thunder, it is the result of the lightning's electrical discharge. The thunder is produced when the air around the lightning bolt expands rapidly due to the high temperature caused by the lightning. This expansion creates a shock wave that travels through the air as sound.

By counting the number of seconds between seeing the flash and hearing the thunder, you are essentially measuring the time it takes for the sound of the thunder to reach you. The longer the time gap, the farther you are from the lightning storm.

In this specific case, if it takes exactly 8 seconds for the sound of the thunder to reach you after you see the flash of lightning, you can use the rule of 1 km per 3 seconds to estimate the distance.

Since the rule states that you are 1 km (or 1000 meters) away for every 3 seconds, you can divide 8 seconds by 3 to find the number of intervals of 3 seconds. That gives you approximately 2.67 intervals.

Now, you can multiply this by the distance covered in each interval, which is 1000 meters.

2.67 intervals x 1000 meters/interval = 2670 meters.

Therefore, based on the given information and the rule, you can estimate that you are approximately 2670 meters (or 2.67 kilometers) away from the lightning storm.