Question

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 ${\vec{v}}_2=(a\hat{i}+7\hat{j})m{s}^{-1}$. If they collide after $2s$, the value of $a$ is

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

Answer: (D)

$AB=\vec{r}=\overrightarrow{r_1}-\overrightarrow{r_2}$
$=(3\hat{i}+5\hat{j})-(-5\hat{i}-3\hat{j})$
$=(8\hat{i}+8\hat{j})m$
$\vec{v}=\overrightarrow{v_2}-\overrightarrow{v_1}$
$=(a\hat{i}+7\hat{j})-(4\hat{i}+3\hat{j})$
$=(a-4)\hat{i}+4\hat{j}$
$\vec{v}=\frac{\vec{r}}{t}$
$(a-4)\vec{i}+\overrightarrow{4j}=\frac{8\hat{i}+8\hat{j}}{2}$
$a=8$