Converting Units: Feet/Second to Miles/Hour and Kilometers/Hour

Converting between different units of speed can sometimes be a bit daunting, especially when you need to switch between the familiar units of feet/second to the more commonly used miles per hour (mph) and kilometers per hour (km/h). This guide provides a straightforward method for performing these conversions using units analysis, a powerful tool in dimensional analysis.

Understanding the Conversion Factors

To effectively convert between units, you first need to understand the conversion factors. Here are some key ones:

1 mile 5280 feet 1 km 1000 meters 1 hour 3600 seconds

Feet/Second to Miles/Hour

Let's take an example to illustrate how to convert 1.467 feet per second (ft/s) to miles per hour (mph).

Step-by-Step Conversion

Multiply by 3600 seconds in an hour: To convert from feet per second to feet per hour, you multiply by the number of seconds in an hour (3600). Divide by 5280 to get miles per hour: After obtaining the value in feet per hour, you divide it by the number of feet in a mile (5280) to convert it to miles per hour.

Let's perform the calculation:

Example Calculation

1.467 ft/s * 3600 s/hr  5281.2 ft/hr5281.2 ft/hr divide; 5280 ft/mile  1.00 mph (approx.)

Feet/Second to Kilometers/Hour

Converting from feet per second to kilometers per hour (km/h) involves a similar process, but use the conversion factors for kilometers and feet first.

Step-by-Step Conversion

Multiply by 3600 seconds in an hour: Again, multiply by 3600 to convert the speed to feet per hour. Divide by 1000 to get kilometers per hour: After obtaining the value in feet per hour, divide it by the number of feet in a kilometer (1000) to convert it to kilometers per hour.

Let's perform the calculation:

Example Calculation

1.467 ft/s * 3600 s/hr  5281.2 ft/hr5281.2 ft/hr divide; 1000 ft/km  5.2812 km/h (approx.)

Detailed Explanation

The key to these conversions lies in using unit conversion factors to manipulate the units. Here's a detailed explanation of the process:

Units Analysis

Units analysis involves multiplying by 1 in the form of conversion factors to cancel out units. For example, to convert 1.467 ft/s to miles/hour, you follow these steps:

1.467 ft/s * (5280 ft/mile) / (3600 s/hr)  1.467 * (5280/3600) mph1.467 * (5280/3600)  1.00 mph

Similarly, for converting to kilometers per hour:

1.467 ft/s * (5280 ft/mile) * (1 mile/1000 km) / (3600 s/hr)  1.467 * (5280/3600 * 1/1000) km/h1.467 * (5280/3600 * 1/1000)  0.52812 km/h

Conclusion

Understanding the conversion between feet/second and miles/hour and kilometers per hour is essential for various applications, from sports to engineering. By mastering these conversions, you can quickly and accurately switch between different units of speed.

For more detailed calculations and further assistance, you can also use online conversion tools or search engines with the query 'feet per second to miles per hour' to get immediate results.

Remember, the key to making these conversions is to consistently apply the appropriate conversion factors and cancel out units appropriately.