Question

You walk exactly 250 steps North, turn around, and then walk exactly 400 steps South. How far are you from your starting point?

Answer 1

150 steps

Step-by-step explanation

to find the final position, we need to add the vectors of displacement

Step 1

Diagram:

Step 2

now, we need to add the vectors

a)let the vectors

U= vector from the start point to the place where he turns around

v= vector from point B to end point

`\begin{gathered} U=\langle0i+250j\rangle \\ v=\langle0i-400j) \end{gathered}`

so, to find the final position we need to add the vectors, component to component

so

`\begin{gathered} U+v=(0i+0i,250j-400j) \\ U+v=\langle0,-150\rangle \end{gathered}`

so, the final position is -150, the negative sign indicates the direction (south) and the magnitud indicates the distance

so, you are 150 steps from your starting point

I hope this helps you