question_answer

Two particles having position vectors \[\overrightarrow{{{r}_{1}}}=(3\hat{i}+5\hat{j})m\]and\[\overrightarrow{{{r}_{2}}}=(-5\hat{i}-3\hat{j})m\]are moving with velocities\[\overrightarrow{{{v}_{1}}}=(4\hat{i}+3\hat{j})m{{s}^{-1}}\]and \[\overrightarrow{{{v}_{2}}}=(a\hat{i}+7\hat{j})m{{s}^{-1}}\]. If they collide after 2 s, the value of a is

A)  2                                            

B)  4

C)  6                                            

D)  8

Correct Answer: D

Solution :

                  \[AB=\overrightarrow{r}=\overrightarrow{{{r}_{1}}}-\overrightarrow{{{r}_{2}}}\]                 \[=(3\hat{i}+5\hat{j})-(-5\hat{i}-3\hat{j})\]                 \[=(8\hat{i}+8\hat{j})m\] \[\overrightarrow{v}=\overrightarrow{{{v}_{2}}}-\overrightarrow{{{v}_{1}}}\]                                 \[=(a\hat{i}+7\hat{j})-(4\hat{i}+3\hat{j})\]                                 \[=(a-4)\hat{i}+4\hat{j}\]                   \[\overrightarrow{v}=\frac{\overrightarrow{r}}{t}\] \[(a-4)\overrightarrow{i}+\overrightarrow{4j}=\frac{8\hat{i}+8\hat{j}}{2}\]                 \[a=8\]