Q. Two particles $A$ and $B$ start moving with velocities $20\, m / s$ and $30 \sqrt{2} m / s$ along $x$-axis and at an angle $45^{\circ}$ with $x$-axis respectively in $x y$-plane from origin. The relative velocity of $B$ w.r.t. $A$
Motion in a Plane
Solution:
$v_{A}=20\, m / s$
$v_{B}=30 \sqrt{2}\, m / s$ along $45^{\circ}$ with $x$-axis
$\vec{v}_{B}=v_{B} \cos 45^{\circ} \hat{i}+v_{B} \sin 45^{\circ} \hat{j}=30 \hat{i}+30 \hat{j}$
$\vec{v}_{B A}=\vec{V}_{B}-\vec{V}_{A}=30 \hat{i}+30 \hat{j}-20 \hat{i}$
$\vec{v}_{B A}=10 \hat{i}+30 \hat{j}$
