Question

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

Answer 1

To solve this problem, we will define speed as the amount of distance traveled per unit of time. We will clear the value of time and in parallel we will convert the Units to an international system to facilitate the calculation since we know the speed of light in a vacuum. The speed defined in terms of distance and time would be

$v = \frac{x}{t} \rightarrow t = \frac{d}{v}$

The speed of light in a vacuum is  $3 * 10 ^ 8m / s$ and 1ft is equivalent to $0.3048m$, so the estimated time would be

$t = \frac{d}{v}$

$t = \frac{0.3048m}{3*10^8m/s}$

$t = 1.02*10^{-9}s$

We know that 1 second is equivalent to $10 ^ 9ns$, therefore

$t = 1.02*10^{-9}s (\frac{10^9ns}{1s})$

$t = 1.02ns$

Therefore the time is 1.02ns