Free Fall: Find Time & Height for Passing Balls

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To determine when the two balls pass each other, set up kinematic equations for both the upward-thrown ball and the dropped ball, equating their displacements to solve for time. The upward ball's motion involves its initial velocity and the effect of gravity, while the dropped ball's motion starts from rest. For the second part, to find when the upward ball reaches its highest point, set its velocity to zero and solve for the corresponding height. The discussion emphasizes the importance of understanding kinematics and applying the correct equations. This approach will yield the necessary time and height values for the scenario described.
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A ball is thrown upward with speed V. At the instant the ball is thrown, second ball is dropped from rest at a height H above the thrown ball, but not directly above it. Ignore air resistance. How much time elapses before the balls pass each other? Find a value of H such that the ball thrown upward is at its highest point when the dropped ball passes.
For the first question, do I need to come up with an equation for both balls and set them equal to each other to find the time when they pass each other? It seems as if I would have two unknowns when I do this. And for the second question do I need to set the velocity equal to 0 to find when the ball reaches its highest point?
 
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For the 1st question, review the kinematics equations again. There is an equation where displacement is expressed as a function of: initial velocity, gravity, and time. By equating this displacement, you can then solve for the time.

For the 2nd question, you are right on!
 
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