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Trajectory means path followed by an object under the influence of gravity.
There isn't any equation of trajectory as such. If path followed by the object is projectile then that equation will be taken under consideration and if path followed is something different then accordingly we will use that trajectory.
The motion of an object under the influence of gravity is determined completely by the acceleration of gravity, its launch speed, and launch angle provided air friction is negligible. The horizontal and vertical motions may be separated and described by the general motion equationsfor constant acceleration.
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