June 9, 2008

Q. 1.5 -- "Problems in General Physics" by I.E. Irodov

$\textbf{Question}$:
Two particles, 1 and 2, move with constant velocities $v_1$and $v_2$. At initial moment their radius vectors are equal to $r_1$and $r_2$. How must these four vectors be interrelated for the particles to collide?

$\textbf{Answer}$:
The only condition required for collision between the two particles is that the particles cover the displacement vector. For this to happen, the relative velocity must be in opposite direction w.r.t to the displacement vector. I.e.

\begin{displaymath}\frac{\vec{r_1} - \vec{r_2}}{\vert\vec{r_1}-\vec{r_2}\vert} = \frac{\vec{v_2} - \vec{v_1}}{\vert\vec{v_2}-\vec{v_1}\vert}\end{displaymath}

Posted by Apurva Sharan at 9:39 PM
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