Question

Melinda is taking a tour through a new city on the tour she walk there .40 miles south 0.65 miles east 0.78 miles north 1.24 miles west then 1.20 miles south at the end of the tour what is Melinda's displacement vector

Answer 1

Answer:

The displacement vector is  $-0.59 \hat i -0.82 \hat j$

Explanation:

Taking East as positive x-axis having a unit vector $\hat i$ and North as positive y-axis having a unit vector $\hat j$.

So, west and south are in negative x and negative y  directions respectively.

As she walks 0.40 miles south, 0.65 miles east, 0.78 miles north, 1.24 miles west then 1.20 miles south.

Scaling 1 mile as 1 unit vector, so 1 mile east = 1 $\hat i$ and so on

Adding all the displacement vectors, we have

$\vec {v} = -0.40 \hat j +0.65 \hat i + 0.78 \hat j -1.24 \hat i - 1.20 \hat j$

$\vec {v} = -0.59 \hat i -0.82 \hat j$

Hence, the displacement vector is  $-0.59 \hat i -0.82 \hat j$