Question

to the driver of a car A moving with velocity va=(3i^-4j^)m/s a second car B appears to have a velocity (5i^+12j^)m/s . The true velocity of tje car B is.​

Answer 1

Given:

To the driver of a car A moving with velocity va=(3i^-4j^)m/s a second car B appears to have a velocity (5i^+12j^)m/s .

To find:

True velocity of car B ?

Calculation:

Let car B have true velocity vector $\vec{v_{B}}$.

Now , the velocity of car B w.r.t A is given in the question , so we can say that :

$\therefore \: \vec{v}_{BA} = \vec{v}_{B} - \vec{v}_{A}$

$\implies \: 5 \hat{i} + 12 \hat{j} = \vec{v}_{B} - (3 \hat{i} - 4 \hat{j})$

$\implies \: 5 \hat{i} + 12 \hat{j} = \vec{v}_{B} -3 \hat{i} + 4 \hat{j}$

$\implies \: \vec{v}_{B} = 5 \hat{i} + 12 \hat{j} + 3 \hat{i} - 4 \hat{j}$

$\implies \: \vec{v}_{B} = 8 \hat{i} + 8 \hat{j}$

$\implies \: \vec{v}_{B} = 8( \hat{i} + \hat{j} )$

So, true velocity of car B is :

$\boxed{ \bold{ \: \vec{v}_{B} = 8( \hat{i} + \hat{j} )}}$