Confusing Old time Measurements =(

[Teenytiny1991]

Homework Statement

A furlong is and old British unit of length equal to 0.125 mi, derived from the length of a furrow in an acre of plowed land. A fortnight is a unit of time corresponding to two weeks, or 14 days and nights. Find the speed of light in megafurlongs per fortnight. (one megafurlong equals a million furlongs).

Homework Equations

speed= distance/time
fur=0,125 mi
for=2 weeks
mg= 1,000,000 fur

The Attempt at a Solution

1 mf/ 1,000,000 fur x 1 fur/0.125 mi x 0.125 mi/ 1fur x 2w/1 for = ... I'm stumped here. i can't understand which way to set it up so that i am only left with mf/for

 

[kuruman]

If you are inexperienced with this, I suggest that you do it in steps instead of trying all at once. I will get you started, but you will have to finish.

You start with what you know. The speed of light is c = 186,000 mile/hr. So you write

$$c=186,000\frac{mile}{hr}$$

Now you are given that

$$1 mile=\frac{1}{0.125}fu$$

Put that in the previous expression to get

$$c=186,000\frac{1}{0.125}\frac{fu}{hr}$$

Now

$$1fu=10^{-6} Mfu$$

Put that in the expression to get

$$c=\frac{186,000\times10^{-6}}{0.125}\frac{Mfu}{hr}$$

Finish the question by proceeding along these lines to get the fortnight in the denominator. Incidentally, you don't really need the 186,000 there. You could as well start with 1 mile/hr to get the conversion factor then multiply the result by 186,000.*** Correction ***

As pointed out by mgb_phys, the speed of light is 186,000 miles/sec. So the conversion is from "sec" to "fortnight". My apologies for the confusion.

 

[CompuChip]

The speed of light in SI units is defined as (approximately) $3 \times 10^8$ m/s.
How many miles per second is this?
So how many furlongs per second?

 

[mgb_phys]

First you need to estimate the answer so you know if you got it right.
A furlong is less than a mile so a speed in furlongs/hour would be a larger number than mi/hour (ie at the same speed you do more furlongs than you do miles) - just like a speed in km/h is a bigger number than in mph.
But a fortnigth is much bigger than an hour so at the same speed you would cover a much bigger distance. So the same speed would be a much bigger number in f/f

Converting is just a matter of fractions.

Assuming you start in miles/sec (c = 186,000 mi/s)
furlongs / fortnight = miles/second * ( fortnight/second) / ( furlongs / mile )

furlongs/mile = 0.125, fortnight/second = 14*24*3600
So 186,000 * (14*24*3600/0.125) =

 

[mgb_phys]

kuruman - slight typo, it's 186,000 mi/SECOND

Teenytiny1991 - using Furlong/Fortnight/Firkin is to teach how to do these sort of conversion. It's just a bit more fun than doing mi/s to m/s or J to eV.