Two particles A and B move with constant velo | vedclass

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(B) For two particles to collide,the relative velocity vector of one particle with respect to the other must be directed along the line joining their

Vedclass · Accepted Answer

$\frac{\vec{r}_1 - \vec{r}_2}{|\vec{r}_1 - \vec{r}_2|} = \frac{\vec{v}_2 - \vec{v}_1}{|\vec{v}_2 - \vec{v}_1|}$

Vedclass · Answer

(B) For two particles to collide,the relative velocity vector of one particle with respect to the other must be directed along the line joining their initial positions.Let the relative position vector be $\vec{r}_{rel} = \vec{r}_1 - \vec{r}_2$.The relative velocity vector is $\vec{v}_{rel} = \vec{v}_2 - \vec{v}_1$.For collision,the direction of the relative velocity must be the same as the direction of the relative position vector.Thus,the unit vectors must be equal:$\frac{\vec{r}_1 - \vec{r}_2}{|\vec{r}_1 - \vec{r}_2|} = \frac{\vec{v}_2 - \vec{v}_1}{|\vec{v}_2 - \vec{v}_1|}$.

Two particles $A$ and $B$ move with constant velocities $\vec{v}_1$ and $\vec{v}_2$. At the initial moment,their position vectors are $\vec{r}_1$ and $\vec{r}_2$ respectively. The condition for their collision is

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