Problem 67 - Chemistry Principles and Practice

Question

A What is the conversion factor that will convert, in one calculation, from \(\mathrm{km} / \mathrm{hr}\) to \(\mathrm{ft} / \mathrm{s}\)

Step-by-Step Solution

Answer

The conversion factor is approximately 0.91134.

Step 1: Understand Units and Conversion

To convert from km/hr to ft/s, we need to know how many feet there are in a kilometer and how many seconds are in an hour. The known conversions are: 1 kilometer = 3280.84 feet, and 1 hour = 3600 seconds.

Step 2: Set Up the Conversion Factor

The conversion factor can be calculated by dividing the number of feet in a kilometer by the number of seconds in an hour: \[\frac{3280.84 \, \text{ft}}{3600 \, \text{s}}\]

Step 3: Calculate the Conversion Factor

Perform the calculation by dividing 3280.84 by 3600:\[\frac{3280.84}{3600} \approx 0.91134\]

Step 4: Conclusion of the Conversion Factor

Thus, the conversion factor from km/hr to ft/s is approximately 0.91134.

Key Concepts

Conversion Factor

A conversion factor is a numerical multiplier used to convert a quantity expressed in one set of units to another, while maintaining the same value. It’s crucial to select the correct conversion factor to ensure accuracy. When converting from one unit to another, such as kilometers per hour (\(\text{km/hr}\)) to feet per second (\(\text{ft/s}\)), understanding and applying a conversion factor is necessary. For example, 1 kilometer equals 3280.84 feet, and 1 hour equals 3600 seconds.

This means that the conversion factor necessary to switch from \(\text{km/hr}\) to \(\text{ft/s}\) is derived by dividing the feet in a kilometer by the seconds in an hour. Hence, the conversion factor becomes:

• \(\frac{3280.84\,\text{ft}}{3600\,\text{s}}\)

Calculating this gives approximately 0.91134, indicating that every kilometer per hour is equivalent to about 0.91134 feet per second.

Kilometer to Feet

When converting kilometers to feet, knowing the precise conversion factor is essential. One kilometer is equivalent to 3280.84 feet. This conversion is based on the international foot, which is a unit of length in both the imperial and U.S. customary systems of measurement.

Understanding this conversion allows for consistent and accurate calculations, whether you’re working on a simple math problem or converting larger distances used in engineering or geographical assignments. To use this in practice, whenever you have a distance measured in kilometers, you multiply it by 3280.84. For example:

• 2 km = 2 × 3280.84 = 6561.68 feet
• 5 km = 5 × 3280.84 = 16404.2 feet

These steps help you convert kilometers into feet accurately and efficiently.

Hour to Seconds

Converting hours to seconds is straightforward because an hour is always equivalent to 3600 seconds. This is computed by understanding the division of hour into minutes and then seconds:

• An hour has 60 minutes.
• Each minute has 60 seconds.

Multiplying these values gives the conversion factor:

• \(60 \times 60 = 3600\)

This means to convert hours into seconds, you multiply the number of hours by 3600. For example:

• 1 hour = 3600 seconds
• 0.5 hours = 0.5 × 3600 = 1800 seconds

This conversion is frequently encountered in problems involving speed and time.

Speed Units Conversion

Speed is the measure of the distance travelled per unit of time. Converting speed from one set of units to another involves using your knowledge of unit conversions. Common speed units include kilometers per hour (\(\text{km/hr}\)), miles per hour (\(\text{mi/hr}\)), meters per second (\(\text{m/s}\)), and feet per second (\(\text{ft/s}\)).

In this context, converting from \(\text{km/hr}\) to \(\text{ft/s}\) requires using the calculated conversion factor approximately 0.91134. The process involves:

• Calculating or using a pre-determined conversion factor.
• Applying it to your speed value.

For instance, to convert 20 km/hr to ft/s, you would multiply by 0.91134:

• 20 km/hr × 0.91134 = 18.2268 ft/s

Understanding these conversions is key for practical applications such as calculating travel times or analyzing motion in physics. Recognizing and accurately applying conversion factors can simplify complex problems and improve problem-solving skills.