Question

A bird moves from point $A$ $(1,-2,3)$ to $B$ $(4,2,3)$. If the speed of the bird is $10\text{m/s}$, then the velocity vector of the bird is:

• A. $5(\hat{i}-2\hat{j}+3\hat{k})\text{m/s}$
• B. $5(4\hat{i}+2\hat{j}+3\hat{k})\text{m/s}$
• C. $(0.6\hat{i}+0.8\hat{j})\text{m/s}$
• D. $(6\hat{i}+8\hat{j})\text{m/s}$

Answer 1

The correct option is D $(6\hat{i}+8\hat{j})\text{m/s}$


Position vector of $A$ $\overrightarrow{r_A}=1\hat{i}-2\hat{j}+3\hat{k}$
Position vector of $B$ $\overrightarrow{r_B}=4\hat{i}+2\hat{j}+3\hat{k}$

Displacement vector $\overrightarrow{r_{BA}}$:
$\overrightarrow{r_{BA}}=\overrightarrow{r_B}-\overrightarrow{r_A}=3\hat{i}+4\hat{j}$

$\therefore$ unit vector in the direction of bird's displacement is:-
$\widehat{r_{BA}}=\frac{\overrightarrow{r_{BA}}}{|\overrightarrow{r_{BA}}|}=\frac{3\hat{i}+4\hat{j}}{\sqrt{3^2+4^2}}=0.6\hat{i}+0.8\hat{j}$

$\because$ Speed of bird $\left(v\right)$ = $10\text{m/s}$
$\overrightarrow{v}=v\times {\hat{r}}_{BA}=10\times (0.6\hat{i}+0.8\hat{j})$
$\therefore \overrightarrow{v}=6\hat{i}+8\hat{j}\text{m/s}$