Problem 8 - College Physics

Question

While driving in an exotic foreign land, you see a speed-limit sign on a highway 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 is approximately 66.96 miles per hour.

Step 1: Convert Furlongs to Miles

We know that 1 furlong is \( \frac{1}{8} \) mile. Therefore, to convert 180,000 furlongs to miles, we multiply the number of furlongs by \( \frac{1}{8} \):\[ 180,000 \times \frac{1}{8} = 22,500 \text{ miles} \]

Step 2: Convert Fortnight to Hours

One fortnight is equal to 14 days, and there are 24 hours in a day. Hence, the total number of hours in a fortnight is given by:\[ 14 \times 24 = 336 \text{ hours} \]

Step 3: Calculate Miles per Hour

Now that we have the distance in miles (22,500 miles) and the time in hours (336 hours), we can find the speed in miles per hour by dividing the total miles by the total hours:\[ \frac{22,500}{336} \approx 66.96 \text{ miles per hour} \]

Key Concepts

Furlong

A furlong is an old English unit of measurement originally used in agriculture. It refers to the length of a plowed furrow, traditionally understood to be about the distance an ox could pull a plow before needing rest. Historically, it evolved to represent \( \frac{1}{8} \) of a mile or about 220 yards. This might seem like an antiquated measure, but it's still in use for horse racing in some countries.

• 1 furlong = 220 yards
• 1 furlong = \( \frac{1}{8} \) mile
• Often used in horse racing

Knowing how to convert furlongs into more commonly used units such as miles proves helpful, especially in situations where the context, such as historical documents or sports, requires this unit.

Fortnight

The term 'fortnight' comes from the Old English 'feowertiene niht,' which means fourteen nights, equating to two weeks. This time unit isn't commonly used in the United States, but it remains popular in other parts of the world, notably the UK. To convert fortnights into more widely used units like hours:

• 1 fortnight = 14 days
• 1 day = 24 hours
• Thus, 1 fortnight = 336 hours (calculated as \( 14 \times 24 \))

Understanding the concept of a fortnight helps in grasping time-planning and duration in historical and cultural contexts, especially when dealing with timelines from literature or British schedules.

Speed Calculation

Calculating speed usually involves understanding the relationship between distance and time. In this expression, speed is the rate at which distance changes over time. It is calculated using the formula:\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]Using our example from the exercise:

• Distance = 22,500 miles
• Time = 336 hours
• Speed = \(( \frac{22,500}{336} \) miles per hour \(\approx 66.96 \))

Understanding this calculation allows you to analyze and compare speeds, whether studying physics, calculating travel times, or converting between different speed units.

Distance Conversion

When converting distances from one unit to another, it's crucial to understand what each unit represents and perform the correct conversion calculations. From the example, converting furlongs to miles is essential for interpreting the speed limit given in furlongs per fortnight:

• 1 furlong = \( \frac{1}{8} \) mile
• 180,000 furlongs = \( 180,000 \times \frac{1}{8} \) miles = 22,500 miles

Distance conversion often involves multiplying or dividing by conversion factors to switch between units such as kilometers to miles, meters to feet, or in this case, furlongs to miles. Practicing these conversions helps improve numerical literacy and understanding of different measurement systems.