Question

Two particles having position vectors $\vec{r}_{1}=(3 \hat{i}+5 \hat{j}) m$ and $\vec{r}_{2}=(-5 \hat{i}-3 \hat{j}) m$ at $t=0$ are moving with velocities $\vec{v}_{1}=(4 \hat{i}+3 \hat{j})$ $m s ^{-1}$ and $\vec{v}_{2}=(a \hat{i}+7 \hat{j}) m s ^{-1}$. For what value of ' $a^{\prime}$ they collide at $=2$ $\sec$

Answer 1

When, they collide then the final position of the particles will same it means,
$\vec{r}_1+\vec{v}_1 t=\vec{r}_2+\vec{v}_2 t$
$(3 \hat{i}+5 \hat{j})+(8 \hat{i}+6 \hat{j})=(-5 \hat{i}-3 \hat{j})+(2 a \hat{i}+14 \hat{j})$

$11 = - 5 + 2 a$
$a = 8$