Hi there i a completely lost with this vectors question
A fruit bat has a speed in still air of 10ms−1. It is pointed in the direction of the bearing 130◦, but there is a wind blowing at a speed of 5ms−1 from the south-west.
Take unit vectors i to point east and j to point north.
(a) Express the velocity b of the bat relative to the air and the velocity w of the wind in component form, giving the numerical values in ms−1 to two decimal places. 
(b) Express the resultant velocity v of the bat in component form, giving numerical values in ms−1 to two decimal places. 
(c) Hence ﬁnd the magnitude and direction of the resultant velocity v of the bat, giving the magnitude in ms−1 to two decimal places and the direction as a bearing to the nearest degree.
Here are some pointers to the right direction. I’ll leave you to fill in the details:
(a) b = 10*cos(130°)*i + 10*sin(130°)*j
w = 5*cos(45°)*i + 5*sin(45°)*j
(b) v = b + w. (add corresponding terms in i and j)
(c) If v = r*i + s*j then |v| = sqrt(r2+s2) and angle = tan-1(s/r)
Let's convert "bearing" into standard degrees....we can convert back at the end.
A bearing of 130° is 320°
A wind from the SW means that the wind is blowing at a 45° angle
a) Velocity of the bat =
[ 10cos (320°) i, 10 sin (320°) j ] =
[ 7.66 i, - 6.43 j ]
Wind velocity = [ 5cos (45°) i , 5 sin (45°) j ] =
[ 3.54 i, 3.54 j ]
b) Velocity of the bat =
[ (7.66 + 3.54) i , ( -6.43 + 3.54 j ] =
[ 11.2 i ,- 2.89 j ]
c) Resultant velocity of the bat =
sqrt [ 11.2^2 + 2.89^2 ] =
Final direction = arctan (-2.89/ 11.2) = -14.47° = -14° [to the nearest degree ]
Converting this to bearing, we have 90 + 14 = 104°