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Chapter 2: Problem 111

An object travels \(80.0 \mathrm{~m} / \mathrm{s}\). How fast is it traveling in miles per hour? \([1 \mathrm{~m}=3.28 \mathrm{ft}, 1\) mile \(=5280 \mathrm{ft}]\)

Short Answer

Expert verified
The object is traveling at approximately \(178.2 \mathrm{~mph}\).

Step by step solution

01

Convert meters per second to feet per second #

To convert the given speed from meters per second to feet per second, we will use the conversion factor 1 m = 3.28 ft. We will multiply the given speed (80.0 m/s) by this conversion factor to obtain the speed in feet per second: \( (\text{80.0 m/s}) \times (\frac{\text{3.28 ft}}{\text{1 m}}) \)
02

Calculate the speed in feet per second #

Now, we will perform the multiplication and get the speed in feet per second: \( (\text{80.0 }) \times (\text{3.28}) = 262.4 \text{ ft/s} \)
03

Convert feet per second to miles per hour #

To convert the speed from feet per second to miles per hour, we will use the conversion factors 1 mile = 5280 ft and 1 hour = 3600 seconds. We will multiply the speed in feet per second (262.4 ft/s) by these conversion factors to obtain the speed in miles per hour: \( (\text{262.4 ft/s}) \times (\frac{\text{1 mile}}{\text{5280 ft}}) \times (\frac{\text{3600 s}}{\text{1 hour}}) \)
04

Calculate the speed in miles per hour #

Perform the multiplication and get the speed in miles per hour: \( (\text{262.4 }) \times (\frac{1}{\text{5280}}) \times (\text{3600}) \approx 178.2 \text{ mph} \) So, the object is traveling at approximately 178.2 miles per hour.

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