Ok, so im having a slight problem with getting to the same resultant as suggested by my book. Perhaps you could help me...
The microlights cruising speed in still air is 45 ms^-1, pointing in the direction of N 54◦ W but flies in a wind speed of 15.2 ms^-1 from a S 28◦ W. We Take i to be 1 ms^-1 due east and j to be 1 ms^-1 due north.
Vm - Velocity Microlight
Vw - Velocity Wind
So Vm has a magnitude of 45 and direction 28◦
The wind comes from S 28◦ W & hence blows towards N 28◦ E for which the direction is -(90◦ -28◦) hence vector Vm has a magnitude 15.2 and direction -62
The components are therefore
Vm = 45 cos(28◦)i + 45sin(28◦)
= 39.7326i + 21.1262J
Vw = 15.2 cos(-62◦)i + 15.2cos (-62)J
=-7.1360i + (-13.4208)J
so i make the resultant
v = Vm + Vw =
39.7326 + (-7.1360)i + 21.1262 + (-13.4208)J
=32.5966i & 7.7054
The suggested resultant is -29.2698i + 39.8711J, so where am i going wrong, thanks guys!