Q3Envn - University Physics with Modern Physics

Question

How many nanoseconds does it take light to travel 1.00 ft in vacuum?

Step-by-Step Solution

Answer

Answer

Light takes 1.016 nanoseconds to travel 1 ft distance in vacuum

Step 1:Speed of light in vacuum

Here,

Light when travels through the vacuum it has maximum speed. The speed of light in vacuum is 3 x 108 m/s. No object in the universe can travel more than this speed.

V= Velocity of light in vacuum (m/s)

D = Distance travelled by light (m)

T = Time taken (s) 

Given data 

Distance in ft = 1 ft 

D = 0.3048 meter 

V = 3 x 108 m/s ( speed of light in vacuum)

Step 2:Calculation of time in nanoseconds

Since, Formula of speed of light is the ratio of distance travelled by the light to the time taken to travelled that distance. 

\(Velocity({\rm{m/s)}} = \frac{{Distace({\rm{m}})}}{{Time({\rm{s}})}}\)

\(\begin{aligned}{c}3 \times {10^8}\,{\rm{m/s}} &= \frac{{0.3048\,{\rm{m}}}}{T}\\T &= \frac{{0.3048\,{\rm{m}}}}{{3 \times {{10}^8}\,{\rm{m/s}}}}\\T &= 0.1016 \times {10^{ - 8}}\,{\rm{S}}\\T &= 1.016 \times {10^{ - 9}}\,{\rm{S}}\\T &= 1.016\,{\rm{nS}}\end{aligned}\)

\(1nS = {10^{ - 9}}\,{\rm{S}}\)

Hence from the above calculation it seems  Light takes 1.016 nanoseconds to travel 1 ft distance in vacuum