1. VECTORS

2. PARALLEL VECTORS
Make one value negative and add together when they are in opposite directions.

3. ACCELERATION AND VELOCITY
Accelerating to the right A V
Decelerating to the right A V
Accelerating to the left A v
Decelerating to the left A

4. RESULTANT VECTOR
A resultant vector represents the sum of two or more vectors

5. THE BOAT
CURRENT
DIRECTION OF BOAT

6. VECTORS AT RIGHT ANGLES
Magnitude: Pythagorean Theorem a2 + b2 = c2 Direction: Tan Ѳ = opposite adjacent c b a

7. PYTHAGOREAN THEORM

8. Ex: A bird flew 4m east then 8m north relative to the ground
Ex: A bird flew 4m east then 8m north relative to the ground. What is the displacement of the bird?
a2 + b2 = c2
4m2 + 8m2 = c2
= c2
√80 =c
C= 8.94m
Tan Ѳ = 8m/4m
Tan Ѳ = 2
Ѳ = Tan-1 2
Ѳ=63.4⁰ Ѳ
C = NE

9. What about the other triangles?
LAW OF COSINE: c² = a² + b² − 2ab cos C LAW OF SINE:

10. Ex: A deer travels 10m east then turns 45⁰ and travels 15m NE
Ex: A deer travels 10m east then turns 45⁰ and travels 15m NE. Find the deer’s displacement.
c² = a² + b² − 2ab cos C
c2 = 10m2 + 15m2-2(10)(15)cos 135
c2 = – (-212)
c2 = 537
c = 23m
45⁰
a = c m = 23m
SinA SinC sinѲ Sin 135⁰
23sinѲ = 15sin 135⁰ Ѳ = 27.5⁰
C = 27.5 ⁰ NE

11. Vector Components
The two perpendicular vectors that combine to form the resultant. Ay A
30° Ax

12. Component formula’s
X – component: Ax = A cos θ Y- component: Ay = A sinθ

13. A car is displaced 300m at 30°NE from its starting position
A car is displaced 300m at 30°NE from its starting position. If it followed Elm street east and then turned north on Willow Street, how far did it travel on each street?
Ax = AcosѲ
Ax =300m cos30
Ax = 259.8m (Elm)
Ay = AsinѲ
Ay = 300m sin 30
Ay = 150m (Willow)
300m
Willow
Elm

14. As the angle of a resultant vector gets larger,
The x component decreases
The y component increases Y Y θ θ X X

15. At 45 degrees the x component is equal to the y component.
45° X