Question

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

Answer 1

Option A is the correct answer.

Step-by-step 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 =
`√(1.2^2+1.6^2) = 2 km`

Angle of resultant with positive X - axis =
`tan^(-1)(1.2/1.6)=36.87^0` = 36.87⁰ east of north.