1. Projectile Motion & Vectors
Vector Components

2. What We Want to Know… What is a vector?
How do we measure the direction of a vector?
How do you find the components of a vector?

3. 2D Coordinate System
With 2D motion, an x-y coordinate plane is a good reference point for determining the magnitude and direction of a vector. +X +Y
In 1D motion, + and – gave direction.
In 2D motion, direction is given with angles (θ).
All angles are measured off of the +x axis. θ

4. Vector Components
Remember, any vector can be resolved into their x and y components. y
Velocity
y-component x
x-component

5. Finding Components
If we know the magnitude and direction of the projectile’s vector, you can find the x and y components. Finding the components is called resolving. y
As long as we don’t change magnitude or direction, we can move a vector.
Hypotenuse v
Vertical
Component
Opposite q x
Adjacent
Horizontal
Component

6. Remember Any vector can be broken down into its components
Velocity Displacement Acceleration
General equation for components: q R y x

7. Practice
How fast must a truck travel to stay directly beneath an airplane that is traveling 29 m/s at an angle of 25° to the ground? X Y
Whenever you have a value at an angle, break it into its components first!
v = 29 m/s
q=25o
Vtruck=?

8. Harder Practice
A daredevil jumps a 32 m wide canyon by driving his motor cycle 20.0 m/s up a 35° ramp.
How fast horizontally is he going?
How much hang time does he get?
What is the greatest height he will reach?
Vx = m/s
t = 1.95 s
Δy = 6.53 m

9. What We Know… What is a vector?
How do we measure the direction of a vector?
How do you find the components of a vector?
What is relative motion?
How do we add/subtract vectors?

10. S.T.A.M.P.
Pirate Dan walks 45 m East, 29 m South, then 8 m West. What single displacement could he have walked?
Williams red wagon flies down a ramp at 4.5 m/s that is angled 15° below the horizontal. If the ramp ends on the edge of a cliff:
How long would it take the wagon to travel 18.8 m horizontally?
How fast vertically would the wagon be going at that point in time?
R = m
θ = °
t = 4.32 s
vf = m/s

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12. Adding Vectors On the same plane
When two vectors are on the same plane, add vectors with simple addition.
Ex. 8m South + 6m North = 2m South (or -2m)
Perpendicular
When two vectors make a right angle with each other. R y q x

13. Adding Vectors not at Right Angles
If something is at an angle, break it into its components! d2 y2 R x2 + d1 y1 x1 +

14. Practice Vector A=4.5m/s @ 35 degrees Vector B=6.5m/s @ -40 degrees
Find A+B

15. S.T.A.M.P.
A ranger leaves his base camp for a ranger tower. He drives 35o south of east for 25.5 km and then drives 65o north of east for 41.0 km. What is the displacement from the base camp to the tower?
R = km
θ = 30.52°

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