Question

Suppose you lived on a planet where the speed of sound in air is 318.75 m/s and the speed of light is 4175 m/s . One night you see a lightning strike in the distance. 20.1 seconds later, you hear thunder. How far is the lightning strike from where you are standing?

Answer 1

6406.88 m

Step-by-step explanation:

To determine the distance of the lightning strike from where you are standing on this hypothetical planet, we will utilize the known speeds of sound and light as well as the time lag between seeing the lightning and hearing the thunder. We'll assume that the speed of light is so fast relative to the speed of sound that the time taken for light to reach you is negligible. Then we'll use the speed of sound and the time delay to find the distance.

Given:

• 
  `v_(sound)=318.75 \ m/s`
• 
  `v_(light) = 4175 \ m/s`
• 
  `t_(lag)=20.1 \ s`

`\hrulefill`

The distance 'd' traveled by a wave (either sound or light) can be calculated using the formula:

`\longrightarrow d=vt \ \big[\because \text{we know} \ v=(d)/(t) \big]`

Where:

• 'v' is the velocity (speed) of the wave
• 't' is the time it takes for the wave to travel that distance

Substitute in our given values and evaluate using a calculator:

`\Longrightarrow d = (318.75 \ m/s )(20.1 \ s)\\\\\\\\\therefore \boxed{d=6406.88 \ m}`

Therefore, the lightning strike is approximately 6406.88 meters away from where you are standing.