This is a simple sim with two balls starting at the same height, one in free fall and one launched with only horizontal velocity. There are two sliders, one to increase the horizontal velocity of the projectile and one to decrease the rate at which they fall (gravity...). This sim shows that the two balls fall vertically at the same rate, indepedent of horizontal velocity.
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ccny-physics-sims/projectile-vs-freefall
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