Question

hakyatwuvhagafahajwuwtt A and B are moving with same constant ( cars) speed 2 m/s in opposite direction. The relative velocityof car A w. r. t car B will be ?​

Answer 1

Given :-

• The magnitude of the velocities of A and B
• $\sf |\overrightarrow{A} | =A = 2m {s}^{ - 1}$
• $\sf |\overrightarrow{B} | =B = 2m {s}^{ - 1}$

To Find :-

• The relative velocity between the cars A and B.

Solution :-

• We are given, the cars A and B are in opposite directions. That means the angle between them is θ = 180°.To find relative velocity between A and B, formula is given by :-

$\sf\red{:\implies R = \sqrt{A^{2} + B^{2} + 2AB\cos\theta}}$

$\small\underline{\pmb{\sf Substituting \: given \: values :-}}$

$\sf\: \: \: \: \: \: \: :\implies R = \sqrt{A^{2} + B^{2} + 2AB\cos\theta}$

$\sf\: \: \: \: \: \: \: :\implies R = \sqrt{ 2^{2} + 2^{2} - 2\times 2 \times 2 (\cos180\degree)}$

$\sf\: \: \: \: \: \: \: :\implies R = \sqrt{4+ 4 - 2 \times 4 (-1) }$

$\sf\: \: \: \: \: \: \: :\implies R = \sqrt{4(1+1+2)}$

$\sf\: \: \: \: \: \: \: :\implies R = \sqrt{2^{2} \times 2^{2}}$

$\sf\: \: \: \: \: \: \: :\implies R = 2\times 2$

$\sf\: \red{ \: \: \: \: \: \: :\implies R = 4}$

$\therefore\:\underline{\textsf{The relative velocity between the cars A and B is \textbf{4m/s.}}}.$