Given ⃗ g g→ has magnitude 18 18 and bearing N 61 ° E N61°E and ⃗ v v→ has magnitude 4 4 and bearing S 37 ° W S37°W, find the vector ⃗ g g→ + ⃗ v v→ as a

THAT is going to need some clarification!     G is 18 @ 61 degrees   and  V is 4  at 37 degrees?    If so:

Break each up into VERT aand HORIZ components and add them together....

Gv =18 sin 61 = 15.74

Vv=   4  sin 37 =  2.40

   Vert = 18.14

 

 

Gh= 18 cos61 =  8.73

Vh=  4  cos37 =  3.19

     Horiz = 11.92

 

Angle =  ARCTAN ( 18.14/11.92) = 56.69 degrees

MAGNITUDE = sqrt ( 18.14^2 + 11.92^2)       =  21.71       (via pythagorean theorem)