Question

If you walk 1.4 km north and then 4.8 km east, what are the magnitude and direction of your resultant displacement?

A. magnitude: 5 km; direction: 73.7 degrees east of north
B. magnitude: 4.6 km; direction: 73.7 degrees east of north
C. magnitude: 5 km; direction: 16.3 degrees east of north
D. magnitude: 4.6 km; direction: 16.3 degrees east of north

Answer 1

A

North and east are perpendicular directions hence we can use them as the basis of our coordinate system. The coordinates of this point can then simply be represented as

P = 1.4 N + 4.8 E (km)

The magnitude can be given by the right triangle formula :

P =
`√(N^2 + E^2)`

= 5 km

Direction = atan(N/E) = 16.3 deg north of east = 73.7 deg east of north