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<title>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?</title>
$1.3.1.$ 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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<img src="1.3.1.png"
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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:
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
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<meta property="og:description" content="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?">
<meta property="og:description" content="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?">
<title>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?</title>
<title>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?</title>
$1.3.1.$ 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?
$1.3.1.$ 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?
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
<center>
<center>
<figure>
<figure>
<img src="1.3.1.png"
<img src="1.3.1.png"
loading="lazy" width="70" />
loading="lazy" width="70" />
</figure>
</figure>
</center>
</center>
The velocity of the first ball after an interval of time $\Delta t$:
The velocity of the first ball after an interval of time $\Delta t$:
$$v_0 = v - g \Delta t$$
$$v_0 = v - g \Delta t$$
The relative velocity of the 1st and 2nd balls will remain constant and equal:
The relative velocity of the 1st and 2nd balls will remain constant and equal:
$$v_\text{average} = g \Delta t$$
$$v_\text{average} = g \Delta t$$
Meanwhile, during the time $\Delta t$, the 1st ball has risen to a height of
Meanwhile, during the time $\Delta t$, the 1st ball has risen to a height of
$$L = v_0 \Delta t - \frac{g \Delta t^2}{2}$$
$$L = v_0 \Delta t - \frac{g \Delta t^2}{2}$$
The time in which they will collide will find how:
The time in which they will collide will find how:
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
