Question

A man goes $10m$ towards North, then $20m$ towards east then the displacement is

• A. $22.5m$
• B. $25m$
• C. $22.36m$
• D. $30m$

Answer 1

The correct option is C

$22.36m$

Step 1: Given Data:

Distance towards north $\overrightarrow{A}$ $=10m$

Distance towards east $\overrightarrow{B}$ $=20m$

Step 2: Formula used:

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

Where, $A=$Magnitude of $\overrightarrow{A}$

$B=$ Magnitude of $\overrightarrow{B}$

$R=$Magnitude of the resultant vector

$\theta =$Angle between $\overrightarrow{A}$ and $\overrightarrow{B}$

Step 3: Calculate the Displacement:

From the figure the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$, that is $\theta =90°$

Final Displacement, $d=\sqrt{\left(10\right){}^2+{\left(20\right)}^2+2\times 10\times 20\times \cos {90}^{°}}$

$=\sqrt{100+400+0}$

$=22.36m$

Hence, option $\left(C\right)$ is the correct answer.