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If you walk 1.2 km north and then 1.6 km east, what are the magnitude and direction of your resultant displacement?


A. magnitude: 2.00 km; direction: 36.9° east of north


B. magnitude: 2.00 km; direction: 53.1° east of north


C. magnitude: 1.1 km; direction: 36.9° east of north


D. magnitude: 1.1 km; direction: 53.1° east of north

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Blacklash

Answer:

 Option A is the correct answer.

Explanation:

  Let the east point towards positive X-axis and north point towards positive Y-axis.

 First walking 1.2 km north,  displacement = 1.2 j km

 Secondly 1.6 km east, displacement = 1.6 i km

 Total displacement = (1.6 i + 1.2 j) km

 Magnitude = [tex]\sqrt{1.2^2+1.6^2} = 2 km[/tex]

 Angle of resultant with positive X - axis = [tex]tan^{-1}(1.2/1.6)=36.87^0[/tex] = 36.87⁰ east of north.

 

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