/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 5 Horses are to race over a certai... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 5

Horses are to race over a certain English meadow for a distance of \(4.0\) furlongs. What is the race distance in (a) rods and (b) chains? (1 furlong \(=201.168 \mathrm{~m}, 1\) rod \(=5.0292 \mathrm{~m}\), and 1 chain \(=20.117 \mathrm{~m}\). )

Short Answer

Expert verified
The race distance is 160 rods and 40 chains.

Step by step solution

01

Convert Furlongs to Meters

Start by converting the race distance from furlongs to meters. The total distance is 4 furlongs, and each furlong is 201.168 meters. Use the conversion formula: \[ \text{Distance in meters} = \text{Number of furlongs} \times \text{meters per furlong} \]Here, \[ \text{Distance in meters} = 4 \times 201.168 = 804.672 \text{ meters} \]
02

Convert Meters to Rods

Now, convert the distance from meters to rods using the conversion factor that 1 rod is 5.0292 meters. \[ \text{Number of rods} = \frac{\text{Distance in meters}}{\text{meters per rod}} \] Plugging in the numbers, \[ \text{Number of rods} = \frac{804.672}{5.0292} \approx 160 \]
03

Convert Meters to Chains

Next, convert the distance from meters to chains. We know 1 chain equals 20.117 meters. Use the conversion formula: \[ \text{Number of chains} = \frac{\text{Distance in meters}}{\text{meters per chain}} \] Substitute the known values to get, \[ \text{Number of chains} = \frac{804.672}{20.117} \approx 40 \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Converting Furlongs to Meters
To convert a distance from furlongs to meters, we first need to understand what a furlong is. A furlong is a unit of distance used in some sports, particularly horse racing. It is an Old English measure and used less frequently today.

To perform this conversion, remember:
  • 1 furlong equals 201.168 meters.
  • Multiply the number of furlongs by this conversion factor.
For example, if the race distance is 4 furlongs, the conversion to meters would be calculated as:
  • 201.168 meters per furlong 鉄� 4 furlongs 脳 201.168 meters/furlong = 804.672 meters.
This tells us the race distance is 804.672 meters. Make sure to perform this step before converting to any other units, as it gives a convenient base for further calculations.
Converting Meters to Rods
Once we have our distance in meters, we can move on to unit conversion into rods. Rods are another historical unit of measure left over from the British Imperial system.

Here's how to convert meters to rods:
  • 1 rod equals 5.0292 meters.
  • To convert from meters to rods, divide the total distance in meters by this value.
For example, if the distance in meters is 804.672 meters:
  • \[ \text{Number of rods} = \frac{804.672\, \text{meters}}{5.0292\, \text{meters per rod}} \approx 160\, \text{rods}\]
Following this method gives us approximately 160 rods. This process helps us understand how larger units of measure, like the meter, relate to smaller, more archaic units like the rod.
Converting Meters to Chains
The final conversion in our series involves converting meters to chains. Chains were historically used by surveyors and also originate from the British Imperial system.

Follow these steps:
  • 1 chain equals 20.117 meters.
  • The conversion from meters to chains is performed by dividing the length in meters by the length of one chain.
Let's convert 804.672 meters to chains:
  • \[ \text{Number of chains} = \frac{804.672\, \text{meters}}{20.117\, \text{meters per chain}} \approx 40\, \text{chains}\]
This calculation shows us that the race distance can be expressed as about 40 chains. Understanding these relationships highlights the interconnected nature of different units of measurement, allowing for greater flexibility in calculation and comprehension.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A typical sugar cube has an edge length of \(1 \mathrm{~cm}\). If you had a cubical box that contained a mole of sugar cubes, what would its edge length be? (One mole \(=6.02 \times 10^{23}\) units.)

A unit of area often used in measuring land areas is the hectare, defined as \(10^{4} \mathrm{~m}^{2}\). An open-pit coal mine consumes 75 hectares of land, down to a depth of \(26 \mathrm{~m}\), each year. What volume of earth, in cubic kilometers, is removed in this time?

An old manuscript reveals that a landowner in the time of King Arthur held \(3.00\) acres of plowed land plus a livestock area of \(25.0\) perches by \(4.00\) perches. What was the total area in (a) the old unit of roods and (b) the more modern unit of square meters? Here, 1 acre is an area of 40 perches by 4 perches, 1 rood is an area of 40 perches by 1 perch, and 1 perch is the length \(16.5 \mathrm{ft}\).

Five clocks are being tested in a laboratory. Exactly at noon, as determined by the WWV time signal, on successive days of a week the clocks read as in the following table. Rank the five clocks according to their relative value as good timekeepers, best to worst. Justify your choice. $$ \begin{array}{lccccccc} \hline \text { Clock } & \text { Sun. } & \text { Mon. } & \text { Tues. } & \text { Wed. } & \text { Thurs. } & \text { Fri. } & \text { Sat. } \\ \hline \text { A } & 12: 36: 40 & 12: 36: 56 & 12: 37: 12 & 12: 37: 27 & 12: 37: 44 & 12: 37: 59 & 12: 38: 14 \\ \text { B } & 11: 59: 59 & 12: 00: 02 & 11: 59: 57 & 12: 00: 07 & 12: 00: 02 & 11: 59: 56 & 12: 00: 03 \\ \text { C } & 15: 50: 45 & 15: 51: 43 & 15: 52: 41 & 15: 53: 39 & 15: 54: 37 & 15: 55: 35 & 15: 56: 33 \\ \text { D } & 12: 03: 59 & 12: 02: 52 & 12: 01: 45 & 12: 00: 38 & 11: 59: 31 & 11: 58: 24 & 11: 57: 17 \\ \text { E } & 12: 03: 59 & 12: 02: 49 & 12: 01: 54 & 12: 01: 52 & 12: 01: 32 & 12: 01: 22 & 12: 01: 12 \\ \hline \end{array} $$

An astronomical unit \((\mathrm{AU})\) is equal to the average distance from Earth to the Sun, about \(92.9 \times 10^{6} \mathrm{mi}\). A parsec \((\mathrm{pc})\) is the distance at which a length of 1 AU would subtend an angle of exactly 1 second of angle of exactly 1 second of arc (Fig. 1-8). A light-year (ly) is the distance that light, traveling through a vacuum with a speed of \(186000 \mathrm{mi} / \mathrm{s}\), would cover in \(1.0\) year. Express the Earth-Sun distance in (a) parsecs and (b) light-years.
See all solutions

Recommended explanations on Physics Textbooks

Thermodynamics

Read Explanation

Fields in Physics

Read Explanation

Waves Physics

Read Explanation

Physical Quantities And Units

Read Explanation

Quantum Physics

Read Explanation

Geometrical and Physical Optics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.