Question

You travel 25 meters east and then travel 48 meters south. What is your total displacement

Answer 1

54.1 m at
`-62.5^(\circ)` (south of east)

Step-by-step explanation:

Displacement is a vector connecting the initial position with the final position of motion.

In this problem, the motion consists of two parts:

- A first movement 25 m east

- A second movement 48 m south

We can therefore write a vector representing the displacement as

`d=(25i-48j)`

where i is the unit vector indicating the east direction and j the unit vector indicating the north direction.

Therefore, the total displacement is just the magnitude of this vector:

`d=√(25^2+(-48)^2)=54.1 m`

And the direction is given by

`\theta=tan^(-1)((d_y)/(d_x))=tan^(-1) ((-48)/(25))=-62.5^(\circ)`