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Ball 1 is thrown into the air and it follows the trajectory for projectile motion shown in the drawing. at the instant it is at the top of its trajectory, ball 2 is dropped from rest at the same height. just before they reach the ground, the velocity of ball 1 has a horizontal component vx and a vertical component vy. ball 2 only has a vertical component. which ball has the greater vertical component?

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Kalahira
The two balls have the same vertical velocity. This is because they begin they're downward motion at the same time. Downward motion is determined by gravity and air resistance in the vertical dimension, which are both equal for the two balls. Therefore, the vertical component of velocity is the same.

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