Question

A light-nanosecond is the distance light travels in 1 ns. Convert 1 ft to light-nanoseconds.

a) 0.305 light-ns
b) 0.1 light-ns
c) 0.3 light-ns
d) 0.05 light-ns

Answer 1

To convert 1 foot to light-nanoseconds, one must understand that light travels 0.3048 meters (1 foot) in about 1.01670336 nanoseconds. The closest given option to this exact number is 1.0 light-nanoseconds, which is option c).

Step-by-step explanation:

The student asked to convert 1 foot to light-nanoseconds. Given that light travels 299,792,458 meters in one second in a vacuum, we know that it travels approximately 1 foot (0.3048 meters) in 1/299,792,458 second. To find out how many nanoseconds that is, we need to convert seconds to nanoseconds (1 second = 1,000,000,000 nanoseconds).

To perform the conversion:

1. Convert 1 foot to meters: 1 foot = 0.3048 meters.
2. Calculate the time taken for light to travel 0.3048 meters: 0.3048 meters × (1 second/299,792,458 meters) ≈ 1.01670336 × 10^-9 seconds.
3. Convert this time into nanoseconds: 1.01670336 seconds × 10^-9 × (1,000,000,000 nanoseconds/1 second) ≈ 1.01670336 nanoseconds.

Therefore, 1 foot is approximately 1.017 light-nanoseconds. However, as we're looking for the closest match from the given options, 1 foot is closest to option c) 1.0 light-ns.