Mathematics 3206
Human Cannon Balls
Name:___________________
Chapter Project – Part 2 (p 78)
Section 2.2
In Section 2.1, you graphed the paths of a human cannon ball shot from a circus cannon. You found his maximum
height and whether or not the path allowed him to clear an 18m high Ferris wheel and land in a safety net.
The following tables show some heights and horizontal distances of a human cannon ball during three different
shots.
Human Cannon Ball
Height (m)
20
15
10
5
0
10
20
30
40
50
60
70
80
90
100
110
Horizontal Distance (m)
SHOT #1
Horizontal
Distance (m)
0
5
10
15
20
Height (m)
3
6.23
9.12
11.67
13.88
D1
D2
1.
How do you know that there is a quadratic relationship between the horizontal distance and the
height for the human cannon ball in shot #1?
2. Determine the equation of the curve of best fit. Where x is the horizontal distance and y is the
height of the human cannon ball during shot #1.
3. Since the net is at a height of 3m, set the height y = 3 in the equation and rearrange to form a
quadratic equation in which one side equals zero.
4. Use the quadratic formula to find the roots of the quadratic equation.
Roots are à
SHOT #2
Horizontal
Distance (m)
0
5
10
15
20
Height (m)
3
8.13
12.72
16.77
20.28
D1
D2
5. How do you know that there is a quadratic relationship between the horizontal distance and the
height for the human cannon ball in shot #2?
6. Determine the equation of the curve of best fit. Where x is the horizontal distance and y is the
height of the human cannon ball during shot #2.
7. Since the net is at a height of 3m, set the height y = 3 in the equation and rearrange to form a
quadratic equation in which one side equals zero.
8. Use the quadratic formula to find the roots of the quadratic equation.
Roots are à
SHOT #3
Horizontal
Distance (m)
0
5
10
15
20
Height (m)
3
10.03
16.32
21.87
26.68
D1
D2
9. How do you know that there is a quadratic relationship between the horizontal distance and the
height for the human cannon ball in shot #3?
10. Determine the equation of the curve of best fit. Where x is the horizontal distance and y is the
height of the human cannon ball during shot #3.
11. Since the net is at a height of 3m, set the height y = 3 in the equation and rearrange to form a
quadratic equation in which one side equals zero.
12. Use the quadratic formula to find the roots of the quadratic equation.
Roots are à
10. Complete the table below.
SHOT #
1.
Curve of
best fit
Quadratic
equation
with y = 3
Roots
Did the
human
cannon ball
land in net?
Why or why
not?
2.
3.