Problem

(a) The speed of light in a vacuum is 2.998 * 108 m>s. Calculate its speed in miles per hour.

Relevant Solution
clock
3m
Play a video:
well everyone in this video, we're gonna go ahead and comfort the MPH unit into meters per second and we're going to go ahead and do this with a method called dimensional analysis. So first, what we're given is the 30 miles per hour and there's going to be an invisible one that they do not write out because it's kind of not necessary. We know that any value divided by one is going to be equal to itself, I'll just go ahead and include this one value just because it'll maybe look make the decision analysis more smoother and more filled. Maybe make a little bit more sense as well. So writing this out, it's going to be 30 miles per one hour and of course this miles of brevity is M. I. And our brave. It is H. R. Okay, so we're gonna go ahead and try to convert this to meters per second which is just M. S. Right, Alright, so go ahead and start off the dementia analysis with the given information which is 30 miles for one hour so we can see that we're converting the distance unit as well as our time units. Doesn't matter which you choose to go ahead and convert first. I'm gonna do the time first or the distance first does not matter because multiplication is cumulative, I'm gonna go ahead and choose to convert my numerator unit first which is my distance. So going from miles into meters which I actually do not know the direct conversion of so take it into baby steps and I'll convert first, the miles into kilometers kilometers two m and that's how I'm going to get into the meters. Okay, so first, like I said, converting from miles to kilometers, so now that for every one kilometer there's going to be 0. to 14 miles and converting that kilometers into meters, I know that for every one kilometer there's going to be 1000 m. Alright, so I've taken care of that meter situation. Let's go ahead and focus on these seconds. So again, just baby steps, I want to first convert my hours and two minutes, so every one hour there's going to be 60 minutes Now, lastly from minutes to seconds. So know that for every one minute there's going to be seconds and as you can see here, our miles will cancel out with our mile unit kilometer with kilometer meter, not meter, sorry, but the hour with the hour and minutes with the minutes, so the remaining answer will have the units of meter on top and second on bottom exactly what we're looking for. So actually doing the math here, I'm gonna go ahead and put in all my values into my calculator And once you do so you should get a value of 13.41 and again mater per second. So that's going to be my final answer for this problem. Thank you all so much for watching