Hello ADY Originally Posted by

**ADY** **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!**

Thanks for showing us all your working, but I'm afraid I don't understand how you arrived at the angles you used in your calculations. $\displaystyle v_m$ is in a direction N $\displaystyle 54^o$ W, so its components are:$\displaystyle -45\sin 54^o$ East and $\displaystyle 45\cos54^o$ North

So:$\displaystyle v_m = -36.41\textbf{i}+26.45\textbf{j}$

And the wind (as you said) blows in a direction N $\displaystyle 28^o$ E, so its components are:$\displaystyle 15.2\sin28^o$ East and $\displaystyle 15.2\cos28^o$ North

So:$\displaystyle v_w = 7.14\textbf{i}+13.42\textbf{j}$

which gives a resultant velocity of:$\displaystyle -29.27\textbf{i}+39.87\textbf{j}$

agreeing with the answer in the book.

Grandad