Question

A man travels $1mile$ due east, $5mile$ due south, $2mile$ due east and finally $9miles$ due north. How far is the starting point?

• A. $3miles$
• B. $5miles$
• C. $4miles$
• D. between $5miles$ and $9miles$

Answer 1

The correct option is B $5miles$

Net eastward displacement $=1+2=3$ miles
Net northward displacement $=-5+9=4$ miles
Net displacement $\overrightarrow{d}=3\hat{i}+4\hat{j}$
$\left|\overrightarrow{d}\right|=\sqrt{3^2+4^2}=5$ miles