Problem 8 - University Physics with Modern 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

180,000 furlongs per fortnight is approximately 66.96 miles per hour.

Step 1: Convert Furlongs to Miles

Since each furlong is equivalent to \(\frac{1}{8}\) of a mile, we need to convert the speed from furlongs to miles. Multiply the given speed, \(180,000\) furlongs, by \(\frac{1}{8}\) to convert it to miles:\[180,000 \times \frac{1}{8} = 22,500 \text{ miles}\]

Step 2: Convert Fortnights to Hours

Next, convert the time from fortnights to hours. A fortnight is 14 days, and one day is 24 hours, so the total number of hours in a fortnight is:\[14 \times 24 = 336 \text{ hours}\]

Step 3: Calculate Miles Per Hour

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

Key Concepts

Furlong

A furlong is a unit of distance that might appear unusual in modern times, but it has its roots in old agricultural practices. Originally, a furlong referred to the length of a furrow in a common field, meaning it was based on how far an oxen team could plow without needing a rest. This unit is still in use today, primarily in horse racing.

• One furlong equals 220 yards.
• This is the same as one-eighth of a mile.
• The conversion to furlong is rare outside of specific contexts.

Thus, if you come across speeds given in furlongs, remember to convert them to units we're more familiar with, like miles, for everyday understanding. In this exercise, for example, converting furlongs to miles helps in interpreting speed limits effectively.

Fortnight

The word "fortnight" is another unit of measure not often seen in daily usage. It stands for a period of 14 days. This term is more commonly used in British English but is quite useful since it represents exactly two weeks.

• A fortnight equals 14 days or 336 hours.
• It is derived from the old English term "fēowerteone niht," meaning "fourteen nights."
• Knowledge of ancient units like fortnights can be beneficial when encountering historical texts or unusual modern references.

In our exercise problem, understanding that a fortnight is equivalent to 336 hours is crucial for converting speed limits from furlongs per fortnight to miles per hour.

Miles per hour

Miles per hour (mph) is a unit of speed most commonly used in the United States and the United Kingdom. It measures the number of miles traveled in one hour. This measurement helps in understanding how fast a vehicle is moving.

• One mile per hour denotes covering one mile in one hour.
• Most speed limit signs you'll see while driving are in miles per hour.
• Being familiar with mph is essential for interpreting vehicular speeds on roads.

In solving the original exercise, converting the speed from furlongs per fortnight to miles per hour makes the speed limit understandable and relatable for those accustomed to this unit of measure.

Speed limits

Speed limits are essential for maintaining safety and order on roads and highways, but the way they are presented can vary significantly depending on the location or even the era being referenced.

• Speed limits express the maximum allowed speed for vehicles under ideal driving conditions.
• They are typically displayed in miles per hour (mph) or kilometers per hour (km/h).
• Unusual unit presentations, like furlongs per fortnight, may require conversion to widely understood measures.

For example, seeing a speed limit of 180,000 furlongs per fortnight on a highway can be puzzling. Hence, converting it to a more familiar unit like miles per hour is important for drivers to comply with regulations appropriately.