Question

Two point masses $1$ and $2$ move with uniform velocities $\overline{v_1}$ and $\overline{v_2}$ respectively. Their initial position vectors $\overline{r_1}$ and $\overline{r_2}$ respectively. Which of the following should be satisfied for the collision of the point masses?

• A. $\frac{\overline{r_2}-\overline{r_1}}{|\overline{r_2}+\overline{r_1}|}=\frac{\overline{v_2}+\overline{v_1}}{|\overline{v_2}-\overline{v_1}|}$
• B. $\frac{\overline{r_1}-\overline{r_2}}{|\overline{r_1}-\overline{r_2}|}=\frac{\overline{v_2}-\overline{v_1}}{|\overline{v_2}-\overline{v_1}|}$
• C. $\frac{\overline{r_2}-\overline{r_1}}{|\overline{r_2}+\overline{r_1}|}=\frac{\overline{v_2}-\overline{v_1}}{|\overline{v_2}+\overline{v_1}|}$
• D. $\frac{\overline{r_2}+\overline{r_1}}{|\overline{r_1}-\overline{r_2}|}=\frac{\overline{v_2}-\overline{v_1}}{|\overline{v_2}+\overline{v_1}|}$

Answer 1

The correct option is B $\frac{\overline{r_1}-\overline{r_2}}{|\overline{r_1}-\overline{r_2}|}=\frac{\overline{v_2}-\overline{v_1}}{|\overline{v_2}-\overline{v_1}|}$

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