**Purpose: **

To find the equation of the curve of best fit formed by a projectile from an algebraic approach and using quadratic regression. This lab will compare forward distance and height by recording data at specified forward distance intervals.

**Materials**

1 spoon

1 small Styrofoam ball

1 large Styrofoam ball

tape

markers

block

Paper

**Pre Lab Question**

What type of function do we expect this trajectory to model? What will the sign of the leading coefficient of the equation of this trajectory be … positive … negative … zero? Explain.

Setup

**Procedure**

1. Orient the paper vertically.

2. Make the origin the lower left corner.

3. Draw three vertical lines on the grid at 3, 6, and 9 inches. Create Horizontal lines at 1 inch intervals ( use the ruler trick)

4. Hang and tape graph paper from the desk edge or the wall.

5. Put catapult (with spoon attached) in front of graph as shown.

7. Place **large ball** in spoon.

8. Release the ball from spoon and observe the projectile path. The other team members must mark the spot where the foam ball crosses the lines (3, 6, 9).

9. Record the heights in data table.

10. Repeat steps 8 and 9 twice more for a total of three trials.

**11. Repeat steps 7 to 10 using small Styrofoam ball. **

**Observations**

Data Large Ball

Vertical Distance at Given Lines

Trial

At x = 0

At x = 3

At x = 6

At x = 9

1

0

30

35

29

2

0

27

29

18

4

0

32

34

26.5

Average

0

29.7

32.7

24.5

Data Small Ball

Vertical Distance at Given Lines

Trial

At x = 0

At x = 3

At x = 6

At x = 9

1

0

28

30

34

2

0

16

19

17

4

0

25

34

26.5

Average

0

23

29.7

25.7

**TI- 83 (Graphing and Equation)**

1). Enter the four data points for the forward distance under L1 and the corresponding four data points for the group average data for vertical distance under L2 using the small ball data.

3). Graph L1 and L2 as a scatter plot. Take a screenshot of your data and insert the graph below. Create a parabolic curve of best fit using QuadReg on the graphing calculator. Record your equation in the appropriate cell below (to the nearest tenth).

5). Repeat this entire process for the large ball and record the curve equation.

Ball Size

Fitted Curve Equation

Small

-1.1 x^{2 }+12x+0.8

Large

-0.8x^{2} +9.5x+0.3

**Insert Graphs Here**

Post Lab Questions

Answer the following questions:

1). Using your group’s curve of best fit equations, predict the height of the ball when the forward distance is 5 inches for both balls.

Large Ball- Height at 5 Inches is

2). Using your group fitted curve of best fit equations, predict the forward distance of the balls when the projectiles hits the ground.

3). Elton and Carol used the same catapult to launch Styrofoam balls. Carol’s ball was twice as large as Elton’s. In this graph, label which path would most likely represent Carol’s ball. Explain your answer.