# Math Tools Chapters 9-12

By Laura Smith

December 5, 2008

Chapter 9- Directional Measurements

Directional measurements are crucial for any journalist to know, especially when it comes to reporting about an accident or a traveling ship for example. The journalist must be able to understand how fast something is happening and how far if that is the case. For example, if the journalist was covering a forest fire, he or she must be able to tell how wide the fire is (how much area it covers), how fast it is spreading, and where it is in terms of direction on a map.

These directional measurements can all be found through time, rate, and distance problems. The order of these can be switched around depending on the solution the journalist needs to find, but the basic formula is still the same. One of the important things to remember when working time, rate and, distance problems is to keep the units of measurement the same. For instance, if the rate is in miles per hour, the time needs to be in hours and the distance in miles. If the time is in minutes, then the journalist needs to divide by 60 to convert it to hours before working out the equation.

The formula for distance is rate multiplied by the time (Distance = rate x time). The formula for rate is distance divided by time (Rate = distance / time). And finally, the formula for time is distance divided by rate (Time = distance/ rate).

Next are speed, velocity, acceleration, g-force, and momentum. While speed and velocity are not the same measurement, the can be used interchangeably. Speed measures how fast something is going and velocity indicates its direction as well. Most likely, a reporter will only have to calculate speed. Average speed is also used by journalists. Average speed is calculated by dividing the distance traveled by the time it took to get there (average speed = distance / time). Instantaneous speed is also used to tell one the speed at exactly a certain moment, seen in a car’s speedometer.

The formula for acceleration is ending velocity minus starting velocity divided by time( acceleration = (ending velocity- starting velocity) / time). The formula for ending velocity is acceleration multiplied by time, plus starting velocity (ending velocity = (acceleration x time) + starting velocity).

A G-force is another measure of acceleration. One “g” stands for the normal force of gravity on Earth’s surface. Acceleration produced by this gravity is measured at 9.8 meters per second per second (32.2 feet per second per second).

Like speed and velocity, weight and mass can be used interchangeably.  Mass is a measure of amount and weight is a measure of the force of gravity pulling on an object. Regardless of gravity, mass always stays the same but weight can change. The metric measure of mass is the kilogram and the metric measure of weight is the Newton. On earth, a Newton is equal to 0.225 lb. on earth.

To find out the ending velocity, you can use what you know- how fast something has been falling. But if you only know the distance something fell, not how fast, you need to find out the ending speed. To do this, the equation needs to be manipulated for acceleration.

Another component is momentum. All moving objects have momentum. It is the force needed to stop an object and is the product of mass and velocity. Momentum = mass x velocity.

Finally, decibels can be used to measure the intensity of sound. One decibel is one-tenth of a Bel, a unit of measure.

Example Problems

Chapter 9

A reporter from the Charlotte Observer went to cover a NASCAR race.  The cars went around a 1.5 mile track . The winner won the race in 3 hours (180 minutes).What was his average speed?

Average speed = 1.5 miles/3 =

Chapter 10

Elon just built another garden on campus. It is a rectangle with a length of 15 feet and a width of 10 feet. What is the perimeter?

Perimeter = (2 x length) + (2 x width)

Perimeter = (2 x 15) + (2 x 10) =

30 + 20= 50 feet

Chapter 11

What is the volume of a suitcase that is 35 inches long, 25 inches wide, and 8 inches tall?

Volume = length x width x height

Volume= 35 x 25 x 8

Volume =7,000 cubic inches

Chapter 12

A reporter took a story on the building of a giant sandbox for children at the local park. He noticed 100 cubic feet of sand was put in the sandbox. How many cubic meters was used.

100 cubic feet x 0.03=3 cubic meters