A student in a rectangular playground sets up an x–y coordinate system with the south–west corner at the origin and the x–axis pointing east.
Starting from the point (5m,0m), the student jogs along four straight paths in the order given below:
1. 18m at 20∘ north of east;
2. 25m due north;
3. 15m at 6π radians south of west;
4. 12m due south.
a. (i) Resolve each of the four displacements into their component form on the chosen axes.
b. (ii) Calculate the student’s final coordinates after completing the sequence.
c. (iii) Determine the magnitude and bearing (angle measured clockwise from north) of the net displacement with respect to the starting point.
d. (iv) If the four displacements were taken in the reverse order, would the final coordinates change? Give a vector–based explanation for your answer.