Answer to Question #239789 in Physics for ela

Question

A cross country skier skis 9 km north and 12 km east on a horizontal show field. How far and in what directions is she from the starting point?

Answer 1

The magnitude of the final displacement can be found from the right triangle in the figure:

$$d = \sqrt{d_1^2 + d_2^2} = \sqrt{9^2 + 12^2} =15km$$

The direction is the following:

$$\theta = \arctan\left( \dfrac{d_1}{d_2}\right)=\arctan\left( \dfrac{9}{12}\right) \approx 37\degree$$

Answer. Magnitude: 15 km. Direction: 37 degrees from the East.