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: 1.1km; direction: 53.1 degrees east of north
B. magnitude: 2.00; direction: 53.1 degrees east of north
C. magnitude: 2.00; direction: 36.9 degrees east of north
D. magnitude: 1.1km; direction: 36.9 degrees east of north

Answer 1

B

Assume north and east as two sides of a right angled triangle. magnitude of the distance is then given by the length of the hypotenuse which is
`√(a^2 + b^2)`

where a = 1.2 km north

and b = 1.6 km east

magnitude = 2 km

Direction is given by the angle between them, that is atan(a/b) = 36.86 deg north of east = 53.1 deg east of north.