Distance between a person and a thunderstorm

[MillieB]

Homework Statement

During a thunderstorm you see lightning before you hear thunder.

Light travels at 300 000 000 m/s in air, you can see lightning almost instantly.

Sound travels at 340 m/s

Jordan hears the sound of thunder 4 seconds after she sees the lightening.

Use the equation that links speed, distance and time to calculate the distance between Jordan and the thunderstorm. Show your working.

Homework Equations

Speed = Distance / Time

The Attempt at a Solution

1. Using the equation D = 4s / 340 m/s (Sound) = 85 m/s

2. Using the equation D = 4s / 300 000 000 m/s (Light speed) = 75 000 000 m/s

3. Therefore using the equations and answers already worked out;

75 000 000 m/s/ - 85 m/s = 74 999 915 m/s

Is this correct? I'm tearing my hair out trying to figure it out. Thanks for any help in advance :)

 

[BvU]

Hello Millie,

Speed = Distance / Time

Is good.

the equation D = 4s / 340 m/s (Sound) = 85 m/s

Is not good. You can check with the dimensions: [second/(m/s)] = [second²/m] which is quite different from [m] ! (Distance, which is what you want)
Speed = Distance / Time so if you multiply by Time on both sides: Speed * Time = Distance !

The above is valid if you can ignore the time needed by the light signal to reach Jordan. And you can check afterwards that that is OK.

If you don't want to ignore that (or aren't allowed to do so), the math becomes a bit more complicated.

 

[MillieB]

Wow thank you SO much for your quick response and taking the time to help me answer.

I think I get what you mean. Using your guidance:

1. Speed = 4s x 340 m/s = 1360 m/s
2. Speed = 4s x 300 000 000 = 1 200 000 000 m/s
3. 1360 m/s + 1 200 000 000 m/s = 1 200001 360 m/s

Is that correct or have I misinterpreted your advice?

 

[scottdave]

Wow thank you SO much for your quick response and taking the time to help me answer.

I think I get what you mean. Using your guidance:

1. Speed = 4s x 340 m/s = 1360 m/s

Is that correct or have I misinterpreted your advice?

As @BvU pointed out, dimensional (and unit) analysis is a powerful tool. You have [Time] x [Length / Time] so your answer is [Length], notr [Length / Time]. So what should be the units on 1360 now? Put the units back in for the others. What can you determine about what light does in a 4 second timeframe?

 

[PeroK]

Wow thank you SO much for your quick response and taking the time to help me answer.

I think I get what you mean. Using your guidance:

1. Speed = 4s x 340 m/s = 1360 m/s
2. Speed = 4s x 300 000 000 = 1 200 000 000 m/s
3. 1360 m/s + 1 200 000 000 m/s = 1 200001 360 m/s

Is that correct or have I misinterpreted your advice?

You are missing something fundamental in working with equations - which is also known as algebra.

If you have speed = distance/time, then:

distance = speed x time

time = distance /speed

Also, although you are given the speed of light, you are also told that light travels almost instantaneously over short distances. This means that you do not need to calculate the travel time of light in this question.

 

[scottdave]

For a RADAR set, the speed of light calculations is important in determining distance, but in comparison with using the speed of sound, it becomes negligible, as others have indicated. For example, it takes less than 5 microseconds for the light from the lightning flash to reach you (for these distances). By not worrying about how long the light takes to get to you, your calculations will be off by only about 2 millimeters.

 

[MillieB]

Thank you to all that contributed. You're ALL superstars