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The rate at which the bucket fills depends on the height from which the water falls and the acceleration of the rain due to gravity in the downward direction.
When the winds blow in the horizontal direction, the rain will then have a horizontal component also added to its velocity which changes the trajectory to a parabolic path. However, this does not affect the rate of the vertical component of the velocity of the falling of water as the height is the same, and the initial velocity is also the same.
Thus, the rate at which the bucket is filling remains unchanged.
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