Oct 10, 2017

The displacement is 118.8 m.

#### Explanation:

Draw that out - like a map. The 45 km portion to the east would be to the right on your paper, from the starting position, A; the KOA is position K; and the 110 km portion to the north would be up on the page to position B. The displacement is the distance from start, A, to end, B.

You should now have drawn a right triangle. So you can use Pythagoras's theorem to find the length of the hypotenuse, line segment AB.

$A {B}^{2} = A {K}^{2} + K {B}^{2}$
$A {B}^{2} = {\left(45 m\right)}^{2} + {\left(110 m\right)}^{2} = 14125 {m}^{2}$

Now taking the sqrt of both sides
$A B = \sqrt{14125 {m}^{2}} = 118.8 m$

I hope this helps,
Steve