Welcome back. Let's check out this practice problem. So, we have a Martian rover that uses radio pulses or signals, which are electromagnetic waves, to communicate with scientists back on Earth. The pulses take about 12 minutes to arrive; presumably, once they hit the little button to transmit information, it takes 12 minutes to arrive. We want to calculate how far apart Mars and Earth are. In this problem, the first thing you should realize is that they're not really asking you to compare the strengths of two fields together. We have no information about the electric or the magnetic field, so, really, this is sort of a different kind of problem in which it's just testing how you can use the information of the speed of light. So here's what's going on here. We know that the definition for velocity is that it's displacement over time, delta \(x\) over delta \(t\). Although, in this case, we know that this \(v\), when we're dealing with electromagnetic waves, is always going to be \(c\), which is the speed of light. So, we can rearrange this equation and say that speed is equal to delta \(x\) over delta \(t\). Basically, we’re told how long it takes for the signals to get to Earth, that’s delta \(t\), and we know what the speed of light is, which is just a constant. So, what they’re asking you to find is delta \(x\), how far apart Mars and Earth are. So let's rearrange this equation here, and so we're going to have delta \(x\) equal to \(c\) times delta \(t\). In our typical studies of motion in one dimension, this was usually a \(v\), velocity times time, but now we're just going to use \(c\). That's all there is to it.
First of all, before we start plugging anything in, we know what the speed of light is. Now we just have to get the time because the time is given to us in minutes, which is 12 minutes. The first thing we have to do here is convert 12 minutes to seconds. All you have to do is multiply by 60, which is seconds per minute. You'll see the units cancel, and you're going to get 720 seconds. That’s what you plug into this equation here. There’s just one little extra step with some units here, and this is just going to be \(3 \times 10^8\) and then you have to do 720. Right? If you didn’t multiply that, remember that the speed is given to us in meters per second, so you can’t multiply meters per second times minutes. So you have to get it into seconds. Anyway, once you work this out here, what you’re going to get here is \(2.16 \times 10^{11}\), and that's in meters. This is perfectly sufficient to write down as an answer, but this is also, if converted, just equal to 216,000,000 kilometers, which is about reasonable for the distance between Earth and Mars.
That's it for this one. Let's keep going.