Forces on a Truss

(Today’s student guest is Erik Lundvall.)

This problem pertains to construction and the way a given force acts upon a given structure. Trusses are triangular pieces used in the construction of some buildings to support weight of other objects such as the weight of the roof for example. In this particular problem the truss extends from the side of the building and is used to support an object. Say you have a business and over the entrance you have a pretty good sized sign advertising your business. The sign sits on a truss that extends over the sidewalk.

If the downward force of the sign towards the building is 250 pounds, the angle of the truss between lines A and B is 20 degrees, and the angle between line A and the sign is 120 degrees, what is the amount of force in pounds that is pulling down on the truss?

Call of Duty 4, Meet Vectors

Today’s student guest blogger is Emilio Inocencio.

One sunny afternoon after completing your homework, you decide to play your favorite video game Call of Duty 4. When you enter your room you find that someone has replaced your Xbox 360 with a machined labeled “Mega 64”. The contraption has a note attached that reads, “To Exit-say the magic word: Delaware.” You notice that the device looks like an old fax machine wirelessly connected to a bicycle helmet. Out of pure curiosity you put the helmet on and wonder what will happen. After a few moments your heart is racing as your mind is being sucked through cyber-space and vivid images of the game Call of Duty 4 flash past your eyes. Suddenly, you find yourself inside a building which looks to be abandoned. To your left you see a .50 caliber sniper rifle pointing outside the window. You then immediately notice that you are in the video game Call of Duty 4! You run to the rifle knowing that you must eliminate the target to prevent nuclear war and ultimately save the world. You look down next to where the rifle is set and see a paper with scribbled notes of the velocities and angles of the bullet and the affecting wind.

The bullet is shot heading N30˚W at a speed of 2600 ft/sec and there is a wind velocity of 30ft/sec with a direction of N45˚W. What is the resultant speed and direction of the bullet?

As you continue to look through your scope you can see the bullet flying towards the target. You gain a faint sense of discomfort and slight taste of blood in your mouth. Just before the bullet hits you whisper the word, “Delaware” and are sucked back into reality. The whole experience has left you hungry and even more prepared to fight the good fight in Call of Duty 4.

Special note: The “Mega 64” idea is not mine and I did infact get permission to use this from the people who created the T.V. show. If you are a fan of many old and new video games I highly recommend buying the DVDs from their website, they are very funny and full of fun times.

Trigonometry at High-Speed

Today’s student guest blogger is Adriana Garcia.

My love for films has taken me to investigate more of the math involved when determining the camera shots needed in specific scenes. In a high-speed car scene, a certain camera angle is needed to fully portray the speed of the car while showing the audience the car going from point A to point B in a viewable amount of time. For example the 2001 film, The Fast and the Furious features many car races. Known for its fun and exciting scenes, the film’s unexpected popularity gave the film a total of $142,542,950 in the box office. But for a specific car race shown in the film between an orange Supra and a red Ferrari 355 Spider, the Ferrari was shown to run a quarter of a mile (1320 feet) in 13.7 seconds. In this scene, what camera angle will be needed to capture the true essence of the car race with the length of 1320 feet off of a 35 feet building? [Ed. note: to clarify, the car is racing either towards or away from the camera.]

Student Guest Problems

I’m going to be posting (starting today) a series courtesy my Pre-Calculus students, who have written a number of trigonometry related problems. They’re not just equations with “solve for x”, but problems based on research of real life situations.

Feel free to make any comments you like and post solutions.