Find the time at which the two balls collide

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To determine the time at which the two balls collide, the equations of motion for both balls must be set equal. The first ball's upward motion can be described by the equation h1 = Vo*t - (1/2)g*t^2, while the second ball's downward motion is h2 = H - (1/2)g*t^2. Setting h1 equal to h2 allows for solving the collision time in terms of Vo, H, and g. For the second part, to find H in terms of Vo and g such that the first ball reaches its peak at the moment of collision, the equation Vo^2 = 2gH must be utilized. This leads to the conclusion that H = Vo^2/(2g) for the specified conditions.
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A ball is thrown straight up from the ground with speed Vo . At the same instant, a second ball is dropped from rest from a height H , directly above the point where the first ball was thrown upward. There is no air resistance.


1-Find the time at which the two balls collide.
Express your answer in terms of the variables "Vo","H" , and appropriate constants..


2-Find the value of "H" in terms of "Vo" and "g" so that at the instant when the balls collide, the first ball is at the highest point of its motion.
Express your answer in terms of the variables "Vo" and "g" .
 
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