Two balls with velocity v are thrown vertically upwards from the same point with time interval \Delta t. How long after the second ball leaves, will they collide?

Solutions of Savchenko Problems in Physics

Aliaksandr Melnichenka
October 2023

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    <h3> Statement </h3>
    <p>
        $1.3.1.$ Two balls with velocity $v$ are thrown vertically upwards from the same point with time interval $\Delta t$. How long after the second ball leaves, will they collide?
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    <h3>Solution</h3>
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The velocity of the first ball after an interval of time $\Delta t$: $$v_0 = v - g \Delta t$$ The relative velocity of the 1st and 2nd balls will remain constant and equal: $$v_\text{average} = g \Delta t$$ Meanwhile, during the time $\Delta t$, the 1st ball has risen to a height of $$L = v_0 \Delta t - \frac{g \Delta t^2}{2}$$ The time in which they will collide will find how: $$t = \frac{L}{v_\text{average}}$$ $$\fbox{$t = \frac{v}{g} - \frac{\Delta t}{2}$}$$

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    <h4>Answer</h4>
    <p>
        $$t = v/g − \Delta t/2$$
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