Question

Two particles $A$ and $B$ start moving with velocities $20m/s$ and $30\sqrt{2}m/s$ along $x-axis$ and at an angle ${45}^o$ with $x-$axis respectively in $xy-plane$ from origin. The relative velocity of $B$ w.r.t. $A$

• A. $(10\hat{i}+30\hat{j})m/s$
• B. $(30\hat{i}+10\hat{j})m/s$
• C. $(30\hat{i}-20\sqrt{2}\hat{j})m/s$
• D. $(30\sqrt{2}\hat{i}+10\sqrt{2}\hat{j})m/s$

Answer 1

The correct option is A $(10\hat{i}+30\hat{j})m/s$

$v_A=20\hat{i}$

$v_B=30\sqrt{2}cos{45}^0\hat{i}+30\sqrt{2}cos{45}^0\hat{j}=30\hat{i}+30\hat{j}$

$v_{BA}=v_B-v_A=10\hat{i}+30\hat{j}$