Math Tools: Chapters 9-12

Chapter 9: Directional Measurements
By Russell Varner
December 4, 2008

I tried to think of some catchy and humorous intro sentence for this, but I couldn’t think of anything better than what Kathleen Woodruff Wickham said to begin Chapter 9: “Time, rate and distance problems are more than middle school headaches.”

It speaks the truth. Directional measurements are an important part of many newspaper stories. Thus, here are some tips to help you out next time you have to include it in an article:

•Don’t simply rely on numbers provided by the people involved in the story. Checking the numbers given to you usually only takes a few basic math problems.
•The basic formula for time, rate and distance is the same for all three, usually involving just a slight variation.
Distance = rate x time
Rate = distance / time
Time = distance / rate
•Mile vs. Knot: A mile equals 5,280 feet and a nautical mile equals 6,080 feet. A knot, on the other hand, is just a measure of speed and one knot is equal to one nautical mile per hour.
•Speed and velocity are not one in the same, though they are often used interchangeably. Speed only measures how fast something is moving, while velocity also includes direction as well as speed. The formula for average speed is as follows: Average speed = distance / time.
•The formula for acceleration is: Acceleration = (ending velocity – starting velocity) / time. You can alter this formula to find any of the other elements. For example, Ending velocity = (acceleration x time) + starting velocity.
•One way to measure acceleration is g-force. Acceleration produced by gravity is measured at 9.8 meters per second per second (9.8 m/s2).
•Say you want to know how fast something was moving but only know how far it fell? To find that, use the following equation: Ending speed = the square root of 2(acceleration x distance).
•Mass and weight are not the same thing. Remember that. Mass is a measure of amount while weight is a measure of the force of gravity pulling on an object.
•Momentum is the force necessary to stop an object from moving. The formula to find momentum is quite simple to remember, too. It is just as follows: Momentum = mass x velocity.
•A decibel (dB) is a unit of measure for the intensity of sound. But remember, sound intensity does not equal “loudness” (“loudness” being a subjective measure of how one’s ears perceive sound).

Problems
1.) You are assigned to cover a marathon for your local newspaper. The runners are supposed to run 25 miles around downtown and the surrounding areas. If the average runner ran at 4 mph, how long would it take him or her to finish the race?
-6.25 hours
2.) You have now been upgraded to covering NASCAR for the newspaper and they want you to cover the Daytona 500. Jimmie Johnson won the race in 4 hours and the drivers have to go 500 miles. What was his average speed?
-125 mph
3.) You have to now drive cross-country in order to cover the Grammy Awards because your editors just can’t figure out what to do with you. It takes you 12 hours to get to Los Angeles while you drive 70 mph and thankfully run into no traffic jams or cops. How far did you just drive?
-840 miles
4.) On just 4 hours of sleep and armed with two 12-packs of Red Bulls, you now have to drive back from Los Angeles. On the way back you witness a big wreck when a truck swerves off the road and into a tree. If the truck weighed 550 pounds and had a velocity of 60, what was the truck’s momentum when it ran into the tree?
-33,000