Help, how to solve this?

Question

James walks in the city. He went four avenues east (0.80 miles), then twenty-four streets south (1.20 miles), then one avenue west (0.20miles), and finally eight streets north (0.40 miles). Find James displacement

Answer 1

Displacement is a vector with a magnitude (distance) and a direction.

In relation to his starting point he went 0.8 miles east and 0.20 miles west, so ending up 0.8 - 0.2 = 0.6 miles east of the starting point

Similarly he ended up 0.8 miles south of his starting point (1.2 - 0.4)

So distance from starting point = √ (0.6² + 0.8² ) = 1 mile

Direction : consider a right triangle, base 0.6 height 0.8. Then the angle his direction makes with the east direction is tan^-1 (0.8 / 0.6) = 53.1⁰.

So his direction is 53.1° SOUTH OF EAST. (or using bearings 90 + 53.1 = 143.1°). Bearing is measured clockwise from north.

So to summarise, displacement = 1 mile 53.1⁰ south of east