Problem 8 - University Physics with Modern Physics

Question

While driving in an exotic foreign land, you see a speed limit sign that reads 180,000 furlongs per fortnight. How many miles per hour is this? (One furlong is \\(\frac{1}{8}\\) mile, and a fortnight is 14 days. A furlong originally referred to the length of a plowed furrow.)

Step-by-Step Solution

Answer

The speed limit is approximately 66.96 miles per hour.

Step 1: Understanding the Units

We need to convert 180,000 furlongs per fortnight into miles per hour. We know that \(1\,\text{furlong} = \frac{1}{8}\,\text{mile}\) and \(1\, ext{fortnight} = 14\, ext{days}\). There are 24 hours in a day.

Step 2: Convert Furlongs to Miles

Convert 180,000 furlongs into miles using the given conversion factor. Calculate: \[180,000 \times \frac{1}{8} = 22,500 \, \text{miles}\] Thus, 180,000 furlongs is equivalent to 22,500 miles.

Step 3: Convert Fortnight to Hours

Convert a fortnight into hours using the given conversions. Calculate: \[14\, \text{days} \times 24\, \text{hours per day} = 336\, \text{hours}\] So, a fortnight is 336 hours long.

Step 4: Calculate Speed in Miles Per Hour

Now that we have the distance in miles and time in hours, divide to find the speed in miles per hour:\[\frac{22,500\, \text{miles}}{336\, \text{hours}} \approx 66.96\, \text{miles per hour}\] So, the speed limit in miles per hour is approximately 66.96 mph.

Key Concepts

Furlong

The term "furlong" might sound a bit archaic, but it’s rooted in agricultural history and has been used as a unit of distance. Historically, a furlong represented the length of a furrow in a plowed field, hence the name. Today, the furlong is precisely defined as 220 yards. To make calculations easier, you can remember that one furlong is equivalent to \(\frac{1}{8}\) of a mile.

• 1 furlong = 220 yards
• 1 furlong = \(\frac{1}{8}\) mile

Because furlongs are not commonly used in most everyday scenarios, converting them to miles is often necessary for practical applications, like speed calculations or distance measurements.

Fortnight

A fortnight is a unit of time equal to 14 days. The term is a contraction of "fourteen nights" and is most commonly used in British English. Despite its practical use in some contexts, it is not as common in everyday international settings.

• 1 fortnight = 14 days
• 1 fortnight = 336 hours (considering 24 hours per day)

Knowing how to convert fortnights to more standard time units like days or hours is critical when calculating speeds or durations over these periods. It becomes particularly useful when interpreting or converting unique speed limits in units per fortnight.

Miles per hour

Miles per hour (mph) is a familiar unit of speed often used in countries like the United States to express both driving and wind speeds. It represents the number of miles traveled in one hour. When converting from unusual speed units like furlongs per fortnight, it becomes necessary to adjust the units into this more common unit for ease of understanding and application.

• mph is a derived unit of speed
• Conversion often needed for practical input into standard road speeds

Utilizing miles per hour in calculations allows for better comparison with common speed indications, especially when traveling.

Speed calculation

Speed calculation can seem tricky with unconventional units, but breaking it down step by step helps. To convert speed from one unit to another, you need to adjust both the distance and time into your desired unit. Start by changing furlongs to miles and fortnights to hours:

• First, convert the distance from furlongs to miles using the relation \(1\,\text{furlong} = \frac{1}{8}\,\text{mile}\)
• Then convert time from fortnights to hours, knowing \(1\,\text{fortnight} = 336\,\text{hours}\)

The converted distance and time can now be used to find speed in miles per hour. Calculate speed as:\[\text{Speed (mph)} = \frac{\text{Distance in miles}}{\text{Time in hours}}\] This provides the speed in a unit that's practical for everyday use, simplifying comprehension and application.