Ball a is thrown vertically upwards with a velocity of v0 . ball b is thrown upwards from the same point with the same velocity t seconds later.
part a
determine the elapsed time t< 2v0/g from the instant ball a is thrown to when the balls pass each other .
express your answer in terms of some or all of the variables v0, t, and the acceleration due to gravity g .

The answer is

Explanation:

If the ball is thrown vertically, the equation of its position is

So setting our coordinate system in the position of throwing , the equation for A is

and for B

where

due to the delay of the throwing between A and B, "t"

.

Now, the balls passing each other means that

then

cancelling some terms...

so

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