Question

Two friends A and B are running parallel to each other . Velocity of A is $\sf{{\blue{3\hat{i} + 4\hat{j} ~ms^{-1}}}}$ and speed of B is $\sf{\blue{20~ms^{-1}}}$ . Find the velocity of B .​

Edit :- Selected the wrong subject by mistake .

Answer 1

Question:-

Two friends A and B are running parallel to each other . Velocity of A is $\sf{{\blue{3\hat{i} + 4\hat{j} ~ms^{-1}}}}$ and speed of B is $\sf{\blue{20~ms^{-1}}}$ . Find the velocity of B.

Given:

Velocity of A = $3 \hat{i} + 4 \hat{j}$

Speed of B = 20m/s

Solution:

Since two friends are running parallel to each other, the direction of A and B would be the same or opposite to each other.

Velocity of A = $3 \hat{i} + 4 \hat{j}$

Find Unit vector in A

$= \frac{3 \hat{i} + 4 \hat{j} }{|3 \hat{i} + 4 \hat{j} |} \\\\ =\frac{3 \hat{i} + 4 \hat{j}} {\sqrt{3^2+4^2}} \\\\= \frac{3 \hat{i} + 4 \hat{j}} {5}$

Velocity of B = Speed x Unit Vector in A

$=20 \times \frac{3 \hat{i} + 4 \hat{j}} {5} \\\\= \cancel{20}~4 \times \frac{3 \hat{i} + 4 \hat{j}} {\cancel{5}} \\\\ =4(3 \hat{i} + 4 \hat{j}) \\\\ = 12 \hat{i} + 16 \hat{j}$

Hence, the velocity of B is $\pm (12 \hat{i} + 16 \hat{j})$