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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
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B
5 miles
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C
4 miles
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D
between 5 and 9 miles
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Solution

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 32+42=5

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