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That means the if you change one you do not necessarily change the other. In the case of the projectile the vertical component is dependent on time (if it is a projectile near a large mass like the earth) gravity acts on it accelerating the projectile in a downward direction. The horizontal component remains the same during the entire flight (if we disregard air resistance and such things).

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Q: The horizontal and vertical components of a projectile's velocity are independent of each other what does this statement mean?
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