Question

A jet is moving at speed of \[180{\text{ km }}{{\text{h}}^{ - 1}}\] . What is its speed in \[{\text{m }}{{\text{s}}^{ - 1}}\].
A. \[{\text{ 10 m }}{{\text{s}}^{ - 1}}\]
B. \[{\text{ 50 m }}{{\text{s}}^{ - 1}}\]
C. \[{\text{ 200 m }}{{\text{s}}^{ - 1}}\]
D. \[{\text{ 500 m }}{{\text{s}}^{ - 1}}\]

Answer 1

Hint:A jet is moving with the speed of \[180{\text{ km }}{{\text{h}}^{ - 1}}\], we have to find this speed of jet in \[{\text{m }}{{\text{s}}^{ - 1}}\]. For this we will convert the units. We will first convert kilometre into metre and then we will convert time of hour into seconds. For finding time in seconds we will first find time in minutes and then convert it into seconds.

Complete step by step answer:
The speed of jet airplanes are usually measured in kilometers per hour because they are one of the fastest moving vehicles. Therefore to avoid calculation problems we usually measure their speed in kilometers per hour. But now we will convert \[180{\text{ km }}{{\text{h}}^{ - 1}}\] into \[{\text{m }}{{\text{s}}^{ - 1}}\]. This can be written as,
\[180{\text{ }} \times {\text{ }}\dfrac{{{\text{km}}}}{h}\]
Since we know that from basic conversion of length, \[1{\text{ km = 1000 m}}\], thus on substituting the value we get,
\[180{\text{ }} \times {\text{ }}\dfrac{{{\text{ 1000 m}}}}{h}\]

Now we will convert time into seconds. We know that one hour of time contains sixty minutes and I minute comprises sixty seconds. Therefore for converting an hour in to second we have to multiply it with, \[\left( {60{\text{ }} \times {\text{ 60}}} \right){\text{ s}}\]. Thus on substituting we get the result as,
\[180{\text{ }} \times {\text{ }}\dfrac{{{\text{ 1000 m}}}}{h}\]
\[\Rightarrow 180{\text{ }} \times \dfrac{{{\text{ 1000 m}}}}{{\left( {60{\text{ }} \times {\text{ 60}}} \right){\text{ s}}}}\]
\[\Rightarrow 180{\text{ }} \times \dfrac{{{\text{ 5 m}}}}{{{\text{18 s}}}}\]
\[\therefore 50{\text{ m }}{{\text{s}}^{ - 1}}\]
Hence the speed of the jet in meters per second is \[50{\text{ m }}{{\text{s}}^{ - 1}}\].

Hence the correct option is B.

Note:We can directly learn the reduced formula for converting kilometre per hour to metre per second by multiplying it with \[\dfrac{5}{{18}}\] and if we want to change from metre per second to kilometre per hour we will multiply it with \[\dfrac{{18}}{5}\]. Make sure to substitute proper values at proper places like substituting seconds in place of hour and metre in place of kilometre.