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I looked up a solution on the
internet where it was claimed that you could treat the process as if
the basketball bounced off the floor and was on its way up by the
time it collided with the tennis ball which at that time would still
be on its way down.
<https://www.physics.harvard.edu/uploads/files/undergrad/probweek/sol1.pdf
This suggests that the timing doesn’t matter. It seems to me thatthe timing does matter.