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 $ are moving with velocities $\vec{ v _{1}}=(4 \hat{ i }+3 \hat{ j }) ms ^{-1}$ and $\vec{ v }_{2}=(a \hat{ i }+7 \hat{ j }) ms ^{-1}$. If they collide after $2\, s$, the value of $a$ is

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

The Correct Option is D

The correct answer is D:8
\(A B=\vec{r}=\vec{r_{1}}-\vec{r_{2}}\)
\(=(3 \hat{i}+5 \hat{j})-(-5 \hat{i}-3 \hat{j})\)
\(=(8 \hat{i}+8 \hat{j}) m\)
\(\vec{v}=\vec{v_{2}}-\vec{v_{1}}\)
\(=(a \hat{i}+7 \hat{j})-(4 \hat{i}+3 \hat{j})\)
\(=(a-4) \hat{i}+4 \hat{j}\)
\(\vec{v}=\frac{\vec{r}}{t}\)
\((a-4) \vec{i}+\vec{4 j}=\frac{8 \hat{i}+8 \hat{j}}{2}\)
\(a=8\)