For a fighter jet to take off from the deck of an aircraft carrier, it must reach a speed of \(62 \mathrm{~m} / \mathrm{s}\) Calculate the speed in miles per hour (mph).

Speed conversion is essentially changing the units of speed from one system of measurement to another. It's a useful skill in chemistry, physics, engineering, and everyday situations. To successfully convert speed, you must understand both the original and target units and use the proper conversion factor.

For instance, when working with speed in a scientific context, it's common to measure it in meters per second (m/s). However, in everyday life, especially in countries that use the Imperial system, speed is often expressed in miles per hour (mph). Understanding how to convert between these units is crucial, especially in disciplines that require data communication to diverse audiences.

To perform a speed conversion, one typically multiplies the given speed by a conversion factor - a number that represents how many of the target units are equivalent to one of the starting units. In our example, the conversion factor from meters per second to miles per hour is approximately 2.23694. This means that one meter per second is equal to approximately 2.23694 miles per hour.

When converting speed from meters per second (m/s) to miles per hour (mph), it is vital to use the correct conversion factor. The conversion factor from m/s to mph is approximately 2.23694.

Here is how the conversion factor is applied: If a fighter jet must reach a speed of 62 m/s to take off, and you want to express this speed in mph, you would multiply the speed value by the conversion factor:
\[62 \, \text{m/s} \times 2.23694 \, \text{mph/m/s} = 138.69028 \, \text{mph}\]

However, it's common to round speed to the nearest whole number for practical purposes. Therefore, the jet's speed can be rounded to approximately 139 mph for easier understanding and communication.

Dimensional analysis, also known as the unit factor method or factor-label method, is a technique used in chemistry and other sciences to convert one set of units to another, to check the consistency of equations, and to solve problems involving quantities. It involves using conversion factors that are written as a fraction of equivalent values, one in each unit, which ultimately allows the user to cancel out units until the desired set of units is achieved.

This technique is not limited to simple conversions. It can be used for multiplying or dividing measurements and can incorporate several conversion factors. For example, in the fighter jet problem, dimensional analysis allowed us to multiply 62 m/s by the factor \(2.23694 \frac{\text{mph}}{\text{m/s}}\) to convert the speed into mph. By doing so, the meters per second units cancel out, leaving only the desired miles per hour unit:
\[\frac{62 \, \text{m}}{\text{s}} \times \frac{2.23694 \, \text{mph}}{1 \, \text{m/s}} = 138.69028 \, \text{mph}\]

Dimensional analysis is a powerful tool for ensuring that calculations involving different units are done accurately, allowing both students and professionals to navigate complex problems confidently.