Edit to “Statement”
en/1.1.4.md
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| @@ -1,6 +1,8 @@ | |||
| ### Statement | |||
| − | $1.1.4.$ Three microphones located on the same straight line at points $A$, $B$, $C$ recorded successively at the moments $t_A > t_B > t_C$ the sound of an explosion that occurred at point $O$, which lies on the segment $AC$. Find the length of the segment $AO$ if $AB = BC = L$. At what point in time did the explosion occur? | ||
| + | $1.1.4.$ Three microphones located on the same straight line at points $A$, $B$, $C$ recorded successively at the moments $t_A > t_B > t_C$ the sound of an explosion that occurred at point $O$, which lies on the segment $AC$. Find the length of the segment $AO$ if $AB = BC = L$. At what point in time did the explosion occur? | ||
| + | |||
| + |  | ||
| ### Solution | |||
| 1\. Let us introduce the following variables | |||
| $$x_B=L-x$$ | |||
| $$t_A=t_B+\Delta t$$ | |||
| 2\. Time of flight of $\gamma$-quantum to counters | |||
| $$t_B+\Delta t=\frac{x}{c}$$ | |||
| $$t_B=\frac{L-x}{c}$$ | |||
| 3\. Solving the equations together, we obtain | |||
| $$\frac{L-x}{c} + \Delta t = \frac{x}{c}$$ | |||
| $$x= \frac{L+c\Delta t}{2}=1.15\text{ m}$$ | |||
| #### Answer | |||
| At a distance $1.15\text{ m}$ from the microphone $A$ | |||
| unchanged lines 21 | |||
| @@ -1,6 +1,8 @@ | |||
| ### Statement | ### Statement | ||
| $1.1.4.$ Three microphones located on the same straight line at points $A$, $B$, $C$ recorded successively at the moments $t_A > t_B > t_C$ the sound of an explosion that occurred at point $O$, which lies on the segment $AC$. Find the length of the segment $AO$ if $AB = BC = L$. At what point in time did the explosion occur? |
$1.1.4.$ Three microphones located on the same straight line at points $A$, $B$, $C$ recorded successively at the moments $t_A > t_B > t_C$ the sound of an explosion that occurred at point $O$, which lies on the segment $AC$. Find the length of the segment $AO$ if $AB = BC = L$. At what point in time did the explosion occur? | ||
|  | |||
| ### Solution | ### Solution | ||
| 1\. Let us introduce the following variables | 1\. Let us introduce the following variables | ||
| $$x_B=L-x$$ | $$x_B=L-x$$ | ||
| $$t_A=t_B+\Delta t$$ | $$t_A=t_B+\Delta t$$ | ||
| 2\. Time of flight of $\gamma$-quantum to counters | 2\. Time of flight of $\gamma$-quantum to counters | ||
| $$t_B+\Delta t=\frac{x}{c}$$ | $$t_B+\Delta t=\frac{x}{c}$$ | ||
| $$t_B=\frac{L-x}{c}$$ | $$t_B=\frac{L-x}{c}$$ | ||
| 3\. Solving the equations together, we obtain | 3\. Solving the equations together, we obtain | ||
| $$\frac{L-x}{c} + \Delta t = \frac{x}{c}$$ | $$\frac{L-x}{c} + \Delta t = \frac{x}{c}$$ | ||
| $$x= \frac{L+c\Delta t}{2}=1.15\text{ m}$$ | $$x= \frac{L+c\Delta t}{2}=1.15\text{ m}$$ | ||
| #### Answer | #### Answer | ||
| At a distance $1.15\text{ m}$ from the microphone $A$ | At a distance $1.15\text{ m}$ from the microphone $A$ | ||
| unchanged lines 21 | |||