Two cars are moving in the same direction with the same speed $30 \mathrm{~km} / \mathrm{hr}$. They are separated by a distance of $5 \mathrm{~km}$. The speed of a car moving in the opposite direction if it meets these two cars at an interval of 4 minutes, will be

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Aicharya · Accepted Answer

The two car (say A and B) are moving with same velocity, the relative velocity of one(say B) with respect
to the other $\mathrm{A}, \overrightarrow{\mathrm{v}}_{\mathrm{BA}}=\overrightarrow{\mathrm{v}}_{\mathrm{B}}-\overrightarrow{\mathrm{v}}_{\mathrm{A}}=\mathrm{v}-\mathrm{v}=0$
So the relative separation between them $(=5 \mathrm{~km})$ always remains the same. Now if the velocity of car (say C) moving in opposite
direction to $\mathrm{A}$ and $\mathrm{B}$, is $\overrightarrow{\mathrm{v}}_{\mathrm{C}}$ relative to ground then the velocity of car $\mathrm{C}$ relative to $\mathrm{A}$ and $\mathrm{B}$ will
be $\vec{v}_{\text {rel. }}=\vec{v}_{c}-\vec{v}$
But as $\overrightarrow{\mathrm{v}}$ is opposite to $\mathrm{v}_{\mathrm{c}}$ So, the time taken by it to cross the cars $A$ and $B$
$
\mathrm{t}=\frac{\mathrm{d}}{\mathrm{v}_{\mathrm{rel} .}} \Rightarrow \frac{4}{60}=\frac{5}{\mathrm{v}_{\mathrm{C}}+30} \Rightarrow \mathrm{v}_{\mathrm{c}}=45 \mathrm{~km} / \mathrm{hr}
$

Two cars are moving in the same direction with the same speed $30 \mathrm{~km} / \mathrm{hr}$. They are…

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