Question

Use the fact that the speed of light in vacuum is about $ 3.00 \times {10^8} $ $ m{s^{ - 1}} $ to determine how many kilometres a pulse from a laser beam travels in exactly nine hours. Answer in units of $ km $ .

Answer 1

Hint :The light has its own speed with which it travels. Speed, time and distance are related to each other in form of an equation. So, if we know the value of any two quantities among these three quantities then we can easily find the value of the third quantity by expressing the unknown quantity in terms of the rest known quantities. In this question, we are given the speed of light and the time taken, we can find the distance that it can cover in that specified time by using the above information.

Complete Step By Step Answer:
The speed of any object is defined as the total distance travelled by that object divided by the time taken by the object to cover that distance. From here you can say that the distance travelled will be equal to the product of speed and time.
We have, $ 1 $ $ hr $ equal to $ 60 \times 60 $ seconds which is $ 3600 $ seconds. Therefore $ 9 $ $ hr $ will have $ 9 \times 3600 = 32400 $ seconds.
Therefore, the distance travelled by the pulse from a laser in nine hours will be $ d = ct $ , where $ c $ is the speed of light and $ t $ is the time required.
 $
  \therefore d = \left( {3 \times {{10}^8}} \right)\left( {32400} \right) \\
  \therefore d = 972 \times {10^{10}} \\
  $
 $ \therefore d = 972 \times {10^{10}} \times {10^{ - 3}} = 972 \times {10^7} $ $ km $
Hence, the distance travelled by a pulse from a laser beam in exactly nine hours will be $ 972 \times {10^7} $ $ km $

Additional Information:
LASER stands for Light amplification by Stimulated Emission of Radiation. It is a device that emits light through optical amplification which is based on stimulated emission of electromagnetic radiation. This laser light is focused at a tight spot. The light emitted by lasers is coherent. The light from a laser can travel a large distance with low divergence.
Uses of laser:
-Communication: laser communication in space, free space optical communication.
-Medicine
-Research: spectroscopy, laser scattering, laser interferometry, microdissections, lidar, fluorescence microscopy.
-Industry: cutting, welding, engraving and bonding.
-Military: target marking.
-Commercial: laser printers, scanner for barcodes, holograms.

Note :
Remember to convert the units appropriately. Here, another way of doing this question was to convert the unit of velocity from $ m{s^{ - 1}} $ to $ kmph $ as follows, $ 1\dfrac{m}{s} = 1\dfrac{{{{10}^{ - 3}}km}}{{\dfrac{1}{{3600}}hr}} = \dfrac{{18}}{5}kmph $ .
Hence, whenever conversion from $ m{s^{ - 1}} $ to $ kmph $ or other way round is required, you can simply multiply or divide by the factor $ \dfrac{{18}}{5} $ according to requirements.