In the game Clash of Clans, wizards surround your troop of barbarians. Spells must be launched to the barbarians to reinforce their power in order for them to defeat the wizards. Materials: popsicle sticks, clothes pins, rubber bands, plastic spoons, glue, candy (spells) Stopwatch, yard stick/measuring tape, Scotch tape, pen/pencil, target Overview: You will launch spells into the air. Using a stopwatch, you will time how long the projectile is in the air. That time will then be used to find an equation to model the flight of the spell. Then the launch device will be moved on top of a desk, and you will use your equation to estimate how far the projectile will travel. Points will be scored based on where your spells land on a target that you place on the floor. You will only have four attempts once the devise is placed on the desk. Directions: 1) Place the devise you designed on the ground. Be careful that it does not change position during tests. Fire a few practice rounds, making sure to pull the device back the same distance each time. It is very important to make sure that your shots are as consistent as possible! 2) You will need one person to be the launcher, one person to be the spotter, and one person to the timer. Make sure you watch where the spell lands the FIRST time.

• Try a few practice runs to make sure that you can hit close to the same spot with each shot. • MAKE SURE TO LAUNCH THE SPELLS THE EXACT SAME WAY E VERY TIME. • Put a piece of tape on the exact mark where each spell lands. 3) Once you get a fairly consistent launch time and launch distance, record 3 official times and their corresponding 3 official distances. Record these values in the table below. Average your three times and distances for the final row. Fill in the times and distances for each trial:

Distance 1: Time 1:

Distance2: Time 2:

Distance3: Time 3:

Average Distance: Average Time: 4) To find the height your spell flew, you must first find the average fall time. Keep in mind, your spell was rising for half of its flight, then fell for the other half. Therefore, to find the time it was falling you must divide your average time by 2.

Average fall time(t): 5) Now, you will find the vertex of the parabola. The equation for free fall of an object is d = ½ gt2 where d is the vertical distance traveled, g is the effect of gravity in meters/s2, and t is the time in the air. The effect of gravity, g, is 9.8 meters/s2, which is 980 centimeters/s2. Plug in gravity and the free fall time you found in step 4 to find the vertical distance your spell traveled. d = You now have the maximum vertical distance your spell traveled, which you know is the y value of the vertex

y of the vertex:

6) To find the x value of the vertex, simply divide your average *horizontal* distance by 2 (from step 3).

x of the vertex: 7) Using the vertex you calculated, the roots of your launch parabola, and following quadratic equation to calculate a.

y = a(x – m)(x – n) 8) Write the final equation for the flight of your spell y = 9) Measure from the floor to the top of a desk.

Desk height: 11) Translate your equation by the height of the desk.

y = 12) Finally, put your equation into a graphing calculator and find where the spell will land. Distance the spell will travel: 13) Place the target where you expect your spell to land. You will be given four attempts. Record your top THREE scores below and ignore the worst result. Part of your grade WILL be based on your points. There are NO PRACTICE RUNS from the desk. Shot 1: ________ Shot 2: ________ Shot 3: ________