1. Chapter 3
Projectile Motion

2. 3.1 Vector and Scalar Quantities
VECTOR QUANTITIES – quantities that have magnitude and direction
EX: force and velocity

3. 3.1 Vector and Scalar Quantities
SCALAR QUANTITIES – quantities that have magnitude, but no direction
EX: mass, volume, time

4. MAGNITUDE – strength of something
“how much?”
DIRECTION –
“which way?”

5. 3.2 Vectors
vector – represented by an arrow whose length is the magnitude of a physical entity and whose orientation shows how the physical entity is directed.

6. MAGNITUDE
less magnitude
more magnitude

7. DIRECTION
EQUAL MAGNITUDE;
OPPOSITE DIRECTION

8. SPEED VS. VELOCITY Velocity has both magnitude and direction.
Speed has only magnitude.

9. You can add the magnitudes of two vectors together to get the magnitude of the resultant vector.

10. RESULTANT the sum of two or more vectors
(and takes into account their directions)

11. For Example: 200 m/s 300 m/s net velocity or resultant velocity

12. Also:
100 m/s +
200 m/s
100 m/s net velocity
or resultant velocity

13. For example:
100 km/hr
10 km/hr
Net Velocity:
90 km/hr

14. OR
100 km/hr
WIND
10 km/hr
Net Velocity:
110 km/hr

15. Not all vectors occur horizontally.
Say the wind was blowing at the plane from the side.
WIND

16. The plane’s velocity is affected by the wind.
Crosswind velocity

17. The plane’s resultant vector would look something like this:

18. By using the parallelogram method, you can represent the resultant of two vectors.

19. Geometric Addition of Vectors
Parallelograms – shapes that have opposite sides of equal length and are parallel.

20. EXAMPLES of parallelograms

21. Create a parallelogram from the two vectors --

22. then connect the corners. The diagonal is the resultant vector.

23. Special Case:
If you have a 90 degree angle, you can use the Pythagorean Theorem to calculate the magnitude of the resultant.

24. PYTHAGOREAM THEOREM
A2 + B2 = C2
C (hypotenuse)
side A
side B

25. For example:
= C2
= C2 ? 3 4
25 = C2
C = C = 5

26. SOH CAH TOA Sine  = opposite/hypotenuse
Cosine  = adjacent/hypotenuse
Tangent  = opposite/adjacent
You can use these when you are missing the lengths of any of the components.

27. 3.3 Components of Vectors
COMPONENT – one of the vectors in a horizontal or vertical direction whose vector sum is equal to the given vector.

28. 3.3 Components of Vectors
Resolution – the process of determining the components of a given vector

29. X X and Y are components (vectors) V is the vector that is resolved V

30. Y V X
Vector V has components X & Y

31. 3.4 Projectile Motion
Projectile – any object that is launched by some means and continues in motion by its own inertia
EX: a cannonball shot from a cannon
a stone thrown in the air
a ball rolling off the table

32. Gravity Gravity acts DOWNWARD
A ball moving horizontally is immune to the effects of GRAVITY on its velocity.
There is no vertical component, only a horizontal component.

33. Gravity
The instant ball is dropped, gravity acts on it,
pulling it toward the center of the earth.
Now it only has a vertical component.

34. 3.5 Upwardly-Moving Projectiles
Figure 3.10
If a projectile had no gravity acting on it, it would move with this path:

35. Gravity changes the path of the projectile:
Gravity pulls the projectile
towards the Earth.

36. Pathways of Projectiles
Objects that move at a constant horizontal velocity while being accelerated vertically down, take a path called a PARABOLA.

37. PARABOLA

38. At each point in its path the projectile has velocity vectors such as those below:
Each velocity vector has a vertical and a horizontal component.

39. Acceleration is constant for a projectile.
Speed and velocity change at each point along the parabolic pathway.
What is the speed of the projectile at the very top of its pathway?
What is the acceleration of the projectile at the very top of its pathway?

40. Air Resistance
Air resistance is another force that acts on projectiles.
It changes the path of a projectile like this:

41. Air Resistance
IDEAL PATH
ACTUAL PATH

42. Air Resistance
If air resistance is negligible, a projectile will rise to its maximum height in the same amount of time it takes it to fall back down.

43. Air Resistance
Without air resistance, the deceleration of the projectile going up is equal to the acceleration of the projectile coming back down.

44. 3.6 Fast-Moving Projectiles: Satellites
Satellite – an object that falls around Earth or some other body because of its tremendous speed, instead of falling into it.
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45. Chapter 3 Key Terms Component Projectile Resolution Resultant
Satellite
Scalar quantity
Vector
Vector quantity