Definition: -this is the shape of the two-dimensional path followed by a projectile.

example: this is seen in basketball shots, cannonball firings, and rocket launchings.

hint: pa

The shape of this path is known as a parabola.

Assumptions: there's no air resistance, and that gravitational pull is constant.

Explanation:

The motion of a projectile can be considered in two separate directions:

In the vertical direction, the projectile would accelerating downwards at a constant rate. (That rate is equal to near  the surface of the earth.) If is the initial velocity of the projectile in the vertical direction, the height of the projectile at time would equal

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In the horizontal direction, the rocket travels at a constant speed. If is the initial horizontal velocity of the rocket, the horizontal position of the rocket at time would be

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Keep in mind that the two-dimensional path of the rocket is more like a function of height over horizontal position , rather than a function of height at time . The goal is to find , an expression of height in terms of horizontal position .

The relationship between and was already determined. Try expressing using with the help of the second equation.

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Replace all occurances of the variable in the expression of using .

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see earlier