A boat travels successively along three displacements in still water: 8 km due east, 6 km at 45∘ north of east, and 10 km due south.
a. (i) On graph paper choose a convenient scale, represent the three displacements in the order given and obtain the approximate resultant displacement R by drawing.
b. (ii) Using trigonometric calculations, determine the exact magnitude of R.
c. (iii) Determine the direction of R measured as a bearing from due east.
d. (iv) Compare the magnitude obtained in (ii) with the scale-drawing result of (i) and comment on any difference.