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| <h3 id="back-link"><a href="../../#1.3">$\leftarrow$Back</a></h3> | | <h3 id="back-link"><a href="../../#1.3">$\leftarrow$Back</a></h3> |
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| <h3> Statement </h3> | | <h3> Statement </h3> |
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| $1.3.1.$ 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? |
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| <h3>Solution</h3> | | <h3>Solution</h3> |
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| 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: |
| $$t = \frac{L}{v_\text{average}}$$ | | $$t = \frac{L}{v_\text{average}}$$ |
| $$\fbox{$t = \frac{v}{g} - \frac{\Delta t}{2}$}$$ | | $$\fbox{$t = \frac{v}{g} - \frac{\Delta t}{2}$}$$ |
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| <h4>Answer</h4> | | <h4>Answer</h4> |
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| $$t = v/g − \Delta t/2$$ | | $$t = v/g − \Delta t/2$$ |
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