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!