Collision: Practice Problem & Solution
Two particles $A$ and $B$, move with constant motion in one dimensional with 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 particle $A$ and $B$ for their collision is: (2015 Re)
Solution Explained:
To solve this problem, we apply the core principles of Collision. Understanding the underlying formula is key to arriving at the correct answer below:
For two particles to collide, their relative position vector must be parallel to their relative velocity vector. Hence, the unit vector of relative position must equal the unit vector of relative velocity: $\frac{\vec{r}_1 - \vec{r}_2}{|\vec{r}_1 - \vec{r}_2|} = \frac{\vec{v}_2 - \vec{v}_1}{|\vec{v}_2 - \vec{v}_1|}$.
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