Question

A man travels $1$ mile due east, then $5$ miles due south, then $2$ miles due east and finally $9$ miles due north. His displacement is

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

Answer 1

The correct option is B $5$ miles

Consider the initial position is at the origin , and North is + Y axis,South being negative Y axis, East is positive X axis and West is negative X axis.
Then starting from origin ,
After 1 miles due east,his coordinates are (1,0)
After 5 miles due south ,his coordinates become (1,-5)
After 2 miles due east , his coordinates are ( 1+2 ,-5) i.e ( 3,-5)
After 9 miles due north , his coordinates are (3,-5+9) i.e ( 3,4)
Hence , distance from the initial position is $\sqrt{3^2+4^2}=5$