Lesson 1

Discover

 

The atlatl (pronounced at-‘lat-al) is a device that was used by the Hopi Indians to hunt game, including rabbits and deer. The atlatl is a leveraging device that increases the acceleration of a spear or dart as it is launched. This launching mechanism increases the effectiveness of the weapon.

 

The design principles of the atlatl can be found in modern tools. One such tool is a ball-thrower, which is used to throw a tennis ball for a dog to chase. Such devices enable the user to throw a ball farther than when the ball is simply thrown with the arm only.

 

Try This 1

 

Students from a high school class are studying the history and mechanics of the atlatl. They spend a few classes constructing atlatls, and then they use the devices in a spear-throwing competition. Atlatl Graph shows the height of a spear over time after being thrown from an atlatl. Answer the following questions based on this graph.

1. From what height was the spear released?
   
   
2.  
   1. What is the maximum height that the spear reaches?
      
      
   2. How long did it take for the spear to reach the maximum height?
      
      
3. How long was the spear in the air? Where do you look on the graph to answer this question, and why do you look there?
   
   
4. The equation of the function represented by the path of the spear is h(t) = −1.42t2 + 3.75t + 1.53, where h(t) is the height of the spear in metres and t is the time in seconds.
   
   
   1. What similarity in numbers is there between this equation and your answers to questions 1 to 3?
      
      
   2. Graph this function on your calculator. Select an appropriate window setting to view the graph.

Save your responses in your course folder.