A visual way to understand vector addition by breaking the vectors down into components and then adding those components together.

2. Trigonometry
Hypotenuse
Opposite
Adjacent

3. Trigonometry
Hypotenuse
Opposite
Adjacent

4. θ
θ
θ
θ
θ
cos
sin
tan
cos
sin
==
=
=
adjacent
opposite
hypotenuse
adjacent
hypotenuse
opposite
Mnemonic device : SOH CAH TOA

5. N
E
10
km
52 °
38 °
10 km [E 38°N]
10 km [N 52°E]

6. SCALARS
# and unit
DISTANCE
SPEED
--
TIME
...
MASS (and other sizes)
WORK / ENERGY, ...
VECTORS
#, unit, and direction
DISPLACEMENT
VELOCITY
ACCELERATION
--
...
FORCE, MOMENTUM,
IMPULSE, ...

9. Length
“ L
”
Lsinθ
L cos θ

10. ADDING VECTORS
Separate each vector into its components.
Put all your Xs together and all your Ys together.
Find how much left-right and how much up-down.
Now, make it back into one big vector –
use Pythagoras and Trig.

14. 30°
40°
L=16m
L
=
9
m
16cos30°
16 sin 30° 9 cos 40°
9sin40°

15. 16cos30°=13.856
16 sin 30°=8 9 cos 40°=6.894
9sin40°=5.785

16. 13.856m
8 m 6.894 m
5.785m
VERTICAL HORIZONTAL
13.856 – 5.785 = 8.071
8 + 6.894 = 14.894

17. 14.894 m
8.071m
16.94 m
94.16894.14071.8 22
=+
°==
=
−
45.28)542.0(tan
894.14
071.8
tan
1
θ
θ

18. 16.94 m
Remember,
the original
problem
was: