Chapter 9: directional measurements
Reporters shouldn’t simply rely on numbers provided by people involved in a story. Checking the numbers in time, rate and distance problems usually involves just some basic math.
In time, rate and distance problems, the basic formula is the same, but components are switched around depending on the solution needed.
Distance = rate * time
Rate = distance / time
Time = distance / rate
Speed and velocity are not the same measurement. Speed measures how fast something is going, while velocity indicates its direction.
The speedometer on a car gives the driver the speed at exactly one moment. This is called instantaneous speed. A more useful figure for a reporter is average speed, which is calculated by dividing the distance traveled by the time it took to get there.
Average speed = distance / time
Acceleration = (ending velocity – starting velocity) / time
Therefore:
Ending velocity = (acceleration * time) + starting velocity
Mass is a measure of amount. Weight is a measure of the force of gravity pulling an object. Mass is the same regardless of gravity.
To determine the speed of an object when it hits the ground. One needs to manipulate the equation for acceleration.
Ending speed = √2(acceleration * distance)
Momentum is the force necessary to stop and object from moving.
Momentum = mass * velocity
Practice problem
Janet Adamson is writing about the speed of a train, which commonly passes through Elrond University’s campus. The train’s acceleration at full throttle is .3 miles per hour per second. If the train is already moving 30 mph, and accelerating at full throttle for 3 minutes, how fast will it be going?
Chapter 10: area measurement
Knowing how to express measurements in an accurate and clear way is vital to good journalism. Analogies are a great way for illustrating measurements that may be otherwise meaningless, but analogies sometimes fail when exact measurements are essential.
Premature of a rectangle
Perimeter = (2 * length) + (2 * width)
Area of a rectangle
Area = length * width
Area of a triangle
Area = .5 base * height
Small spaces are measured in square inches or square feet. Larger areas, such as parking lots, are measured in square feet, square yards or square rods.
144 inches = 1 square foot
9 square feet = 1 square yard
30 square yards = 1 square rod
160 square rods = 1 acre
1 acre = 43,560
640 = 1 square mile
The radius of a circle is the distance from any edge to the middle. Knowing the radius is key to finding the circumference, or the distance around. Knowing the radius is also necessary to find the area of a circle.
Circumference = 2Pi * radius
Area = Pi * radius^{2}
Practice problem
Elrond University’s quidditch field is 120 yards long with two end zones of 5 yards each and a width of 75 yards. What is the field’s parameter and area?
Chapter 11: volume measurements
Volume measurements play a key role in many articles, especially on the business beat.
Rectangular solid
Volume = length * width * height
Common liquid conversion
2 tablespoons = 1 fluid ounce
½ pint = 8 ounces, or 1 cup
1 pint = 16 ounces, or two cups
2 pints (32 ounces) = 1 quart
2 quarts (64 ounces) = ½ gallon
4 quarts (128 ounces) = 1 gallon
1 U.S. standard barrel = 31.5 gallons
1 U.S. gallon = 4/5 Imperial gallon
British or Canadian barrel = 36 Imperial gallons
Cord
A cord is commonly used to measure firewood, and is defined as 128 cubic feet.
Ton
There are three different types of tons. A short ton is 2000 pounds. The British ton is the long ton, which is 2240 pounds. There is also a third type of ton called the metric ton, equal to 1000 kilograms, or 2204.62 pounds.
Practice problem
A famous book of college reviews sent one of their workers to Elrond University to measure the size of a student dorm room. The rectangular room is 8 feet by 12 feet by 12 feet. How many cubic feet is the dorm room?
Chapter 12: the metric system
Outside the United States, most of the world uses the metric system for nearly every type of measurement. The unit names are meter (length), gram (mass) and liter (volume).
Length (metric) | U.S. | |
1 millimeter [mm] | 0.03937 in | |
1 centimeter [cm] | 10 mm | 0.3937 in |
1 meter [m] | 100 cm | 1.0936 yd |
1 kilometer [km] | 1000 m | 0.6214 mile |
Area (metric) | U.S. | |
1 sq cm [cm^{2}] | 100 mm^{2} | 0.1550 in^{2} |
1 sq m [m^{2}] | 10,000 cm^{2} | 1.1960 yd^{2} |
1 hectare [ha] | 10,000 m^{2} | 2.4711 acres |
1 sq km [km^{2}] | 100 ha | 0.3861 mile^{2} |
Volume/ Capacity (metric) | U.S. | ||
1 cu cm [cm^{3}] | 0.0610 in^{3} | ||
1 cu decimeter [dm^{3}] | 1,000 cm^{3} | 0.0353 ft^{3} | |
1 cu meter [m^{3}] | 1,000 dm^{3} | 1.3080 yd^{3} | |
1 liter [l] | 1 dm^{3} | 2.113 fluid pt |
Mass (metric) | U.S. | ||
1 milligram [mg] | 0.0154 grain | ||
1 gram [g] | 1,000 mg | 0.0353 oz | |
1 kilogram [kg] | 1,000 g | 2.2046 lb |
Temperature
(1.8 * °C ) + 32 = °F
.56 * (°F – 32) = °C
Practice problem
While studying abroad, Janet Adamson was asked to cook her host family dinner. She needs approximately 3 pounds of flower to bake dessert. Will a 1 kg bag be enough? Why or why not?