Question

How many miles does light travel in one hour? The speed of light is $1.86 \times {10^5}$ miles per second.

Answer 1

Hint:A light year is defined as the distance travelled by a light ray in one complete year. So, we have to calculate the distance travelled by a light ray in one complete hour in miles in order to find the number of miles travelled by a light ray in an hour. Distance travelled by a light ray is calculated by using the formula: \[Distance = \left( {Time} \right)\left( {Speed} \right)\].

Complete step by step solution:
We know that the speed of light is$1.86 \times {10^5}$ miles per second.
Time duration $ = 1$hour
So, Distance travelled by a light ray in one hour \[ = \left( {Time} \right)\left( {Speed} \right)\]
\[ = \left( {1hour} \right)\left( {1.86 \times {{10}^5}miles/\sec } \right)\]
Number of minutes in one hour $ = 60\min $
Number of seconds in one minute $ = 60\sec $
Number of seconds in one complete hour $ = $$3600\sec $
So, Distance travelled by a light ray in one hour \[ = \left( {1hour} \right)\left( {1.86 \times {{10}^5}miles/\sec } \right)\]
\[ = \left( {3600\sec } \right)\left( {1.86 \times {{10}^5}miles/\sec } \right)\]
On solving further,
\[ = \left( {6696 \times {{10}^5}miles} \right)\]
This can also be written in scientific notation as: \[\left( {6.696 \times {{10}^8}miles} \right)\]
Hence, A light ray travels \[\left( {6.696 \times {{10}^8}miles} \right)\] in an hour.

Note: We also know the speed of light in metres per second unit as $3 \times {10^8}m{s^{ - 1}}$. The given problem can also be solved by first converting the speed of light from $m{s^{ - 1}}$to $miles{\left( {second} \right)^{ - 1}}$ and then multiplying it with the time duration in seconds so as to get the distance travelled by light in one complete year in miles. Care should be taken while converting units of distance from metres to miles and while carrying out subsequent calculations.