Original Lesson retrieved from www.teachengineer.org Adapted by Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia (© 2010)

Strawkets & Quadratics You need to: Find a buddy. Get a materials basket.

In your materials basket: 2 sheets of paper 2 drinking straws 2 pairs of scissors Stopwatch A tape dispenser (You will need to share with another group if your group does not have one.)

Each buddy gets a sheet of paper. Assembling Procedure Each buddy gets a sheet of paper. Fold the paper in half (hamburger style). Unfold. Cut the paper along the fold line.

Assembling Procedure Wrap one piece of paper around a pencil starting from the eraser and working toward the tip. The paper should make a cone shape.

This end is the "nose" of the strawket. Assembling Procedure Tape the tube of paper near each end so it keeps its shape then remove the pencil. (Note: Make sure the final length of paper tubing is a few centimeters shorter than the straws. Cut the paper tubing with scissors, if necessary.) Pinch and fold the smaller end of the tube over and tape it so it is airtight. This end is the "nose" of the strawket.

Assembling Procedure Design and fasten a set of wings or fins to the strawket using the other half sheet of paper and tape. Maximum height of the wings should be 8.5 inches. Minimum height of the fins should be 2 inches.

Personalize your strawket (including your name). Assembling Procedure Personalize your strawket (including your name).

Rules No strawkets may be launched while the previous student retrieves his/her strawket. No strawkets should be launched at another person. No launching until instructed to begin.

Blast-Off Procedure Insert the straw into the strawket — holding onto the straw, not the paper part of the strawket — aim at the 8 foot mark, and blow. While one buddy is launching, the other buddy collects and records the following data: Time (in seconds – rounded to the nearest tenths) Launching height (in inches) **To convert inches to feet with decimals, divide the number of inches by 12. Round to the nearest hundredth.

Repeat process but switch roles. Blast-Off Procedure Repeat process but switch roles. Buddy A Buddy B Height Time (to the nearest tenth of a second) Initial (launching height) 0 sec. Maximum (vertex) 8 ft. 5.25 ft 4.83 ft 0.5 sec. 0.3 sec.

After collecting the data: ANAlysis After collecting the data: Exchange the data. Use your launching height and time for the vertex to write a quadratic function, h(t) = -16t2 + vot + ho. based on 32 ft/s2 gravity initial velocity initial height time

-16(_______)2 + vo (_______) + (_______) = 8 ANAlysis A. Plug in vertex’s time and launching height. 0.5 0.5 5.25 -16(_______)2 + vo (_______) + (_______) = 8 vertex’s time launching height

-16(_______)2 + vo (_______) + (_______) = 8 ANAlysis B. Solve for the initial velocity (vo). 0.5 0.5 5.25 -16(_______)2 + vo (_______) + (_______) = 8 vo = 13.5

h(x) = -16t2 + (_______) t + (_______) ANAlysis C. Plug in initial velocity and launching height to write a quadratic function for your strawket. 13.5 5.25 h(x) = -16t2 + (_______) t + (_______) initial velocity launching height You have your quadratic function!! 

Analysis 3. Use the quadratic formula to determine the time when the strawket hit the ground. h(x) = -16t2 + 13.5t + 5.25 v v v (13.5) (13.5) (-16) (5.25) (-16) v x = -0.29, 1.13

unneeded part of parabola maximum height (vertex) initial height (ho) unneeded part of parabola Why? equal time equal time ground level

Analysis 4. Graph both sets of data (including initial, maximum, and landing points). 9 8 7 6 5 4 3 2 1 Height (in feet) 0 0.5 1 1.5 2 Time (in seconds)