Question

The Concorde is the fastest airline used for commercial service. It can cruise at 1450 miles per hour (about two times the speed of sound or in other words, mach 2). What is it in m/s?
A) $644.4\;{\text{m/s}}$
B) $80\;{\text{m/s}}$
C) $40\;{\text{m/s}}$
D) None of the above

Answer 1

In This question, the concept of the conversion factor is used, that is use the conversion factor to convert miles/hour to meter/second. As we know that the Mach number is the ratio of the speed of the object and the speed of the sound.

Complete step by step solution:
In this question, we are given the speed of an airline Concorde in ${\text{miles per hour}}$. We have to convert the speed from ${\text{miles per hour}} \to {\text{metres per seconds}}$. We can use the following formula:
$\Rightarrow 1\;{\text{miles per hour}} = 0.447\;{\text{m/s}}......\left( 1 \right)$
Speed of the airlines is $1450\;{\text{miles per hour}}$. So, using equation (1),
$\Rightarrow 1450{\text{ miles per hour}} = 1450 \times 0.447\;{\text{m/s}}$
This is equal to ${\text{648}}{\text{.15}}\;{\text{m/s}}$
Other way we can calculate this is by using the following conversion formula:
$\Rightarrow \dfrac{1}{{2.237}}\;{\text{miles/hour}} = 1\;{\text{m/s}}......\left( 2 \right)$
After substituting $1450{\text{ miles per hour}}$in equation (2), we get:
$\Rightarrow \dfrac{{1450}}{{2.237}}\;{\text{miles/hour}} = 648.19\;{\text{m/s}}$
So, equation (2) and equation (3) give us the answer from miles per hour to metres per seconds.

Since none of the options display this answer and we also have an option for ‘none of the above’, we will choose option (D).

Additional information:
Since it is given that the conversion from miles per hour to metres per seconds will be the speed that is about twice the speed of sound, we can also use this to find the approximate solution. The speed of sound is. So, after doubling the speed we get
$\Rightarrow 343\;{\text{m/s}} \times 2 = 686\;{\text{m/s}}$
Since it is not exactly twice the speed of sound, we can use it as an approximate answer.
Another manner can be where we use the conversion from ‘mach 2’ which is another unit for the speed of sound.
$1\;{\text{mach}} = 343\;{\text{m/s}}$
So, $1\;{\text{mach}}$is equal to the speed of sound. So, this will give the same answer as above.

Note: The different units can be used to depict the speed of light such as miles per hour, or metres per seconds, or kilometres per hour or mach and so on. The conversion from one unit to another can be easily done provided you know the conversion formula.