Question

Find the displacement if you walk 2 miles east then walk 4 miles north

Answer 1

The displacement is about 4.47 miles

Step-by-step explanation:

Displacement

Is the vector that represents the difference in positions that an object has moved on.

If the object was at position
`\vec p_1` and ended up in the position
`\vec p_2`, then the displacement is:

`\vec d=\vec p_2- \vec p_1`

The magnitude of d is the length of the vector. Given its rectangular coordinates (dx,dy), then the magnitude is:

`\mid d\mid=√(dx^2+dy^2)`

If you walk 2 miles east from the origin, your new position is (2,0). When you now walk 4 miles north, your final position is (2,4).

The displacement is:

`\vec d=(2,4)-(0,0)=(2,4)`

And its magnitude is:

`\mid d\mid=√(2^2+4^2)`

`\mid d\mid=√(4+16)`

`\mid d\mid=√(20)`

`\mid d\mid\approx 4.47\ miles`

The displacement is about 4.47 miles