A hiker starts from point O and completes the following journey on level ground. All directions are given with reference to the usual compass directions, where east is taken as the positive x-axis and north as the positive y-axis.
• 2.0 km due east
• 3.0 km at an angle of 30∘ north of east
• 1.5 km due south
• 4.0 km at an angle of 45∘ south of west
• 2.5 km due north
Answer the following parts:
a. (i) Represent each of the five displacement legs in component form xi^+yj^.
b. (ii) Determine the resultant displacement vector of the entire journey in component form.
c. (iii) Calculate the magnitude of this resultant displacement and state its direction as a bearing measured clockwise from north.
d. (iv) Find the distance and direction that the hiker must walk in a single straight line to return directly to the starting point O. Express the direction as a bearing measured clockwise from north.