incoming yap fest:

okay so here's what i do personally (easier than tip to tail + cosine and more relevant to module 5)

so you can consider each vector kind of like a right angle triangle. you have TWO perpendicular components (cause phys only does 2d vectors)

so you want to break down each vector into

and

components using trigonometry.

for instance, a vector angled at 30 degrees above the horizon with a magnitude of, say, 45 can be broken down into the component parallel to the horizon and the component perpendicular to the horizon

.

View attachment 42620
for this, the perpendicular component is given by

while the parallel component is given by

. with this, you can sum all the perpendicular components and parallel components separately and use pythagoreas to get the resultant (make sure to inverse tan the components to get the final vector)

example:

vector a has a magnitude of 75 and is pointing at N30E, vector B has a magnitude of 30 and is pointing at S45W.

View attachment 42621
you can sum the horizontal components as such:

and then vertical:

and then to get the resultant vector, you use pythagoreas

and inverse tangent for direction

i suggest this method for two reasons

1. it's easier when you have many different vectors (collisions in module 2)

2. you will decompose vectors anyways in module 5 for projectile motion

ALSO I LOWKEY FORGOT BEARINGS BUT LIKE I HOPE THIS MADE SENSE

you can also make a table of the x and y components.

EDIT: PLEASE DO NOT FORGET YOUR AXIS LABELS LIKE I DID HERE I'M TOO CEEBS TO DO ANYTHING