##### THE parabola

A parabola is a two-dimensional, symmetrical curve, which is approximately U-shaped.

A two-dimensional space is a simplified model of the world we live in. The two dimensions are commonly called length and width. A square is a two-dimensional space.

The everyday world that we live in actually is a three-dimensional space with length, width and depth. A cube is a three- dimensional space.

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Symmetrical - A geometric shape or object is symmetric if it can be divided into two or more identical pieces.

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A vertex is a point where two or more curves, lines, or edges meet.

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Projectile Motion

Projectile motion is a form of motion in which an object (such as a basketball) is launched near the earth's surface, and upon being launched (shot), it moves along a curved path under the action of gravity only. For the purpose of these examples, air resistance is too small to worry about.

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In projectile motion, the horizontal motion and the vertical motion are independent of each other. The horizontal component of the velocity of the projectile remains unchanged throughout the motion. This is the principle of compound motion established by Galileo in 1638.

Assuming the standardized value for gravity and ignoring air resistance, this means that an object falling freely near the Earth's surface increases its velocity by (32 ft/s or about 22 mph) for each second of its descent. Thus, an object starting from rest will attain a velocity of 32 ft/s) after one second, approximately 64 ft/s) after two seconds, and so on.

Ignoring air resistance, any and all objects, when dropped from the same height, will hit the ground at the same time, a point proved by Gaileo. Eventually Gaileo was arrested, convicted and sentanced to house arrest for saying that the earth revolved around the sun.

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