Question

A disoriented physics professor drives 3.22 km north, then 4.75 km west, then 1.90 km south. find the magnitude and direction of the resultant displacement, using the method of components.

Answer 1

It can be noted that the directions west and north are perpendicular to each other. hence we can use the right angle formula for calculating total distance in these directions. Also South is just negative north. This technique is called euclidean distance norm. It is the basis of Cartesian coordinate system.

Total distance = 3.22 N + 4.75 W +1.90  S

= 1.32 N + 4.75 W

D = $\sqrt{N^2 + W^2}$

D = 4.93 Km

direction = atan(N/W) = 15.53 deg north of west