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# Kinematics

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.

Note by Nihar Mahajan
9 months ago

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Equation 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 $$\dfrac {2x} g =(2y-t)(t)$$. · 9 months ago