How many nanoseconds does it take light to travel 1.00 ft in vacuum? (This result is a useful quantity to remember.)

Video transcript

Hey everyone. So today we're being asked to calculate the time in microseconds that it takes from light that it takes for light to travel from the sun to planet Venus, if the two planets, the two heavenly bodies are 67 million miles apart and were given the speed of light to help us with our calculations. So the first thing we want to do before anything is write down a few conversion factors. We need to remember that one mile is equal to 1.609, 3, 4 km, one kilometer, It's the same thing as 1000 m. And since we need to go to two microseconds, we need to know the conversion that one second is equal to to the sixth microseconds. So with all that in mind, let's start. We have we know that the distance between the two planets are 67 and let's write this in blue. The distance between them is 67 million miles. So let's first convert that two m because we are looking for meters per second because that's what our velocity of light is. So that led us to their calculations. So to convert this, we take and convert this first two kilometers. So six point or 1.6 or 934 kilometers for every one mile. So our miles terms will cancel out And we know that we have 1000 m for every one km meaning our kilometer terms will also cancel out and simplifying. We get our answer to be 1.78 times 10 to the 11th meters. So that is the distance between the two heavenly bodies and meters. Now, we should also recall that according to the cinematics, the equation for distance is simply velocity by time. Therefore time is equal to distance by velocity. And we actually already have these values. We have the distance. We just calculated it. It is 1.07, 8 times 10 to the 11th m and the velocity is just the speed of light because we are talking about light years after all the time it takes from light to travel from the sun to the planet. We're talking about light speed. So three times 10 to the 8th m/s. Not late years. Sorry, my bad. But simplifying that we get an answer of 359. seconds. Now that we have our answer in seconds we can use the conversion factor from earlier from seconds to microseconds to finally get our answer. So we I'm not going to use that color. We multiply by 10 to the sixth. Microseconds for every one second so our seconds will cancel out and we will be left with a final answer of 3.5933 times 10 to the eighth Microseconds or in other words answer choice. D 359.33 million microseconds. I hope this helps. And I look forward to seeing you all in the next one