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What force is most responsible for the path of an object during projectile motion?

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The gravitational force.

In fact, the motion of the projectile is composed by two independent motions:
- on the horizontal direction, it is a uniform motion (with constant speed)
- on the vertical direction, it is a uniformly accelerated motion, where the vertical acceleration g is given by the gravity exerted by the Earth on the projectile.

For this reason, the composition of the two motions results in a parabolic trajectory.
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