Question

A group of soldiers walked 15 km north from their camp, then covered 10 km more due east. a. What was the total distance walked by the soldiers? b. Determined the total displacement from the starting point. Used graphical method (scale: 5 km : 1 cm)

Answer 1

(a) The total distance can be found as follows:

$$s_{tot}=s_1+s_2=15\ km+10\ km=25\ km.$$

(b)

We can find the magnitude of the total displacement from the Pythagorean theorem:

$$d=\sqrt{d_x^2+d_y^2}=\sqrt{(10\ km)^2+(15\ km)^2}=18\ km.$$

We can find the direction of the resultant displacement from the geometry:

$$\theta=tan^{-1}(\dfrac{d_y}{d_x})=tan^{-1}(\dfrac{15\ km}{10\ km})=56.3^{\circ}\ N\ of\ E.$$