Question

A body moves due East with velocity $20kmh{r}^{-1}$ and then due North with velocity $15kmh{r}^{-1}$. The resultant velocity in $kmh{r}^{-1}$

• A. $5$
• B. $15$
• C. $20$
• D. $25$

Answer 1

The correct option is D

$25$

Step 1: Given Data

Initial velocity, $\overrightarrow{u}$$=20$ $\overrightarrow{i}$

Final velocity, $\overrightarrow{v}$$=15$$\overrightarrow{j}$

Step 2: Formula used

Resultant velocity vector$=$$\overrightarrow{v}-\overrightarrow{u}$

Step 3: Find the magnitude of the resultant velocity vector

$\left|\overrightarrow{v}-\overrightarrow{u}\right|$ $=$$\sqrt{v^2+u^2}$

$=$$\sqrt{\left({15}^2+{20}^2\right)}$

$=\sqrt{225+400}$

$=25kmh{r}^{-1}$

Hence, the resultant velocity is $\mathbf{25}\mathbf{}\mathit{k}\mathit{m}\mathit{h}{\mathit{r}}^{\mathbf{-}\mathbf{1}}$

Hence, option $\left(D\right)$ is correct.