Two bodies begin a free fall from the same height, \(t\) seconds apart. How long after the first body begins to fall will the both bodies be \(x\) meters apart?

The particles never reach the ground and ignore air resistance.

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## Comments

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TopNewestEquation for displacement of first body is \(s_1=\dfrac 1 2 gy^2\) where \(y\) is the time(in sec).

Equation for displacement of second body is \(s_2=\dfrac 1 2 gz^2\) where \(z\) is the time(in sec).

We have \(y-z=t\) or \(z=y-t\) and \(s_1-s_2=x\).

We can rewrite this as \(\dfrac 1 2 gy^2-\dfrac 1 2 gz^2=x\) or \(\dfrac 1 2 gy^2-\dfrac 1 2 g(y-t)^2=x\).

Now simplifying we have \(\dfrac {2x} g =(2y-t)(t)\).

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Same :)

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