Question

A man 'A' moves in the north direction with a speed 10 m/s and man 'B' moves in ${30}^0$ North of East with 10 m/s. Find the relative velocity of B w.r.t. A.

Answer 1

Man 'A' moves in north direction with speed 10 m/s

So we can write

${\overrightarrow{v}}_a=0\hat{i}+10\hat{j}$

Now for other person

Man 'B' moves in 30 North of East with 10m/s

so we can write

${\overrightarrow{v}}_b=10\cos 30\hat{i}+10\sin 30\hat{j}$

${\overrightarrow{v}}_b=5\sqrt{3}\hat{i}+5\hat{j}$

Now the relative velocity of B with respect to A is given by

$v_{ba}=\overrightarrow{b}-\overrightarrow{a}$

$v_{ba}=(5\sqrt{3}\hat{i}+5\hat{j})-(0\hat{i}+10\hat{j})$

$v_{ba}=5\sqrt{3}\hat{i}-5\hat{j}$

Magnitude is given by

$|v_{ba}|=\sqrt{(5\sqrt{3}{)}^2+(-5{)}^2}$

$|v_{ba}|=10m/s$

Therefore the relative velocity of B w.r.t A is 10 m/s