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It's parabolic. More specifically, it's half a parabola, with a vertex at the point of origin.

You see, horizontal and vertical velocity are independent of each other. This means that the projectile will more horizontally at a constant velocity (ignoring wind resistance) equal to its initial velocity. At the same time, the projectile is accelerated downward at a rate of 9.8 m/s2 (approximately). Since it undergoes constant acceleration, it increases in velocity every second exponentially, giving it a parabolic curve.

As an interesting side note, since horizontal and vertical velocity are always independent of each other, any velocity (really, any vector) can be represented as its horizontal and vertical components, allowing one to add up the individual components and to find a resultant vector quantity.

Here's an example drawing of the curve described: http://www.staff.amu.edu.pl/~romangoc/graphics/M2/1-projectile-motion/M2-3.gif

Keep in mind that if the point of origin is at a greater vertical level than the ground, the projectile will fall all the way to the ground, past the horizontal axis.

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