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2013 IEBC www.iebcnow.org. Parabola. 2013 IEBC SLATE Demonstration Curricula www.iebcnow.org. 1. Parabola. A parabola is a plane conic section curve formed by the intersection of a right circular cone and a plane parallel to a side of the cone.

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2013 IEBC

www.iebcnow.org

Parabola

2013 IEBC

SLATE Demonstration Curricula

www.iebcnow.org

1

Parabola

A parabola is a plane conic section curve formed by the intersection of a right circular cone and a plane parallel to a side of the cone.

Mathematically, a parabola is the two-dimensional graph of a second-degree or quadratic equation or function of the form.

2013 IEBC

SLATE Demonstration Curricula

www.iebcnow.org

2

Conic Sections and Shapes

Parabola

Parallel to the side

Hyperbola

Circle

Ellipse

2013 IEBC

SLATE Demonstration Curricula

www.iebcnow.org

3

Parabolic Curve Applications

2013 IEBC

SLATE Demonstration Curricula

www.iebcnow.org

4

Trajectory for Launched Object

2013 IEBC

SLATE Demonstration Curricula

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5

Trajectory: NASA Zero G Aircraft
• Parabolic Flight
• 30 thousand feet
• 28
• 26 Zero-G
• 24
• 22
• 20
• 0 20 40
• Duration (seconds)

Plane at 45 °

Plane at 45 °

1.8-G

1.8-G

2013 IEBC

SLATE Demonstration Curricula

www.iebcnow.org

6

Source: NASA-MSFC

Parabolic Concentration

2013 IEBC

SLATE Demonstration Curricula

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7

Concentration Examples

Technology satellite

Satellite antenna

Source: NASA-GRC

2013 IEBC

SLATE Demonstration Curricula

www.iebcnow.org

8

Concentration Examples

Trough solar dish

Source: Sandia National Laboratories

2013 IEBC

SLATE Demonstration Curricula

www.iebcnow.org

9

Parabolic Dispersion

2013 IEBC

SLATE Demonstration Curricula

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10

Dispersion Examples

A parabolic headlight uses a parabolic reflector surrounding a bulb to focus light and then disperses the light by the shape of the lens.

2013 IEBC

SLATE Demonstration Curricula

www.iebcnow.org

11

Parabolic Curves in Sports

Source: www.Pics4Learning.com

2013 IEBC

SLATE Demonstration Curricula

www.iebcnow.org

12

Parabolic Curves at Home

2013 IEBC

SLATE Demonstration Curricula

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13

Architecture

San Francisco Golden Gate Bridge

2013 IEBC

SLATE Demonstration Curricula

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14

Storming Castle Pi: Overarching Problem

The Raving Irrationals are trying to overtake the Castle of Pi. They want to launch burning bales of hay into the castle to drive out the citizens of Pi.

When the catapult arm is pulled back to ground level, the hay bale is launched at a distance of 100 feet west of the castle wall. The wall is 35 feet high. The bale clears the wall by a height of 15 feet and lands inside the castle, which is also 100 feet from the wall.

The Irrationals come under attack and must retreat from this site. Their new position is 70 feet southwest of the wall. They need to relaunch; however, the wall on this side is 45 feet high. If the castle is 120 feet in diameter, will the hay bales land inside the castle wall or fly over it?

2013 IEBC

SLATE Demonstration Curricula

www.iebcnow.org

15

Application of a ParabolaUsed with permission by:

2013 IEBC

SLATE Demonstration Curricula

www.iebcnow.org