Question

A cross-country skier skis 1.00km north and then 2.00km east on a horizontal snowfield. how far and in what direction is she from the starting point?

Answer 1

a) We can find the resultant displacement of the cross-country skier from the Pythagorean theorem:

$$R = \sqrt{R_x^2 + R_y^2} = \sqrt{(2.0 km)^2 + (1.0 km)^2} = 2.24 km.$$

b) We can find the direction of the displacement vector from the geometry of the problem:

$$tan\theta = \dfrac{R_x}{R_y},$$ $$\theta = tan^{-1} (\dfrac{R_x}{R_y}) = tan^{-1} (\dfrac{2.0 km}{1.0 km}) = 63.4^{\circ}.$$

Answer:

a) $R = 2.24 km.$

b) $\theta = 63.4^{\circ}.$