1. Projectile Motion

2. Let’s Review
A projectile is an object upon which only force acting is GRAVITY. Remember that the direction of gravity is always DOWNWARD.
Types of projectiles:
Objects that are dropped
Objects that are launched horizontally
Objects that are launched upward at an angle

3. Characteristics
The path of a projectile is called a trajectory and is shaped like a parabola.
There are two components of motion, horizontal and vertical.
These components are independent of one another.

4. Horizontal Projectiles
A horizontal projectile is launched with an angle of 0o to the horizontal.
What have we learned so far? The horizontal velocity is constant. The vertical velocity is changing.

5. Sum It Up None Gravity, 9.8 m/s2,down Constant Changing
Horizontal Motion
Vertical Motion
Acceleration
Velocity
None
Gravity, 9.8 m/s2,down
Constant
Changing

6. Projectiles Launched at an Angle
Once the projectile is launched, the only force acting is Gravity.
As with horizontally launched projectiles, the horizontal velocity is constant.
The vertical velocity is changing. As the projectile travels upward, the vertical velocity decreases. It reaches 0 m/s at the top of its flight. The vertical velocity increases as the object travels downward.
These velocity components can be represented with vectors.

7. Factors Affecting Projectile Motion
How does the initial velocity affect the flight of a projectile?
Initial Velocity
Time
Distance traveled
 20
 30
 40
 50

8. The greater the initial velocity, the greater the hang time, the longer the horizontal distance

9. How does the initial velocity effect the flight of a projectile?
Angle
Time of flight
Horizontal Distance
Vertical Distance 20 30 45 60 70 90

10. Initial Velocity Observations
What do you notice about the complimentary angles? They have the same horizontal distance.
Which angle produces the maximum range (horizontal distance)? 45 degrees
From your observations, which angle produces the maximum height? 70 degrees

11. Describing Motion with Numbers

12. Describing Motion with Numbers
What was the initial velocity in the upward direction? Let’s determine this velocity using vectors. To do this:
Add the vectors graphically. Label all information.
Draw the resultant.
Use the Pythagorean Theorem to determine the resultant. This is the INITIAL VELOCITY.
To determine the angle, use TRIG functions
22.9 m/s
19.6 m/s
59°
12 m/s

13. Example 1 cos 60 = vx/40 Vx = 20 m/s Sin 60 = vy/40 Vy = 34.6 m/s
A water balloon is launched with a velocity of 40 m/s at an angle of 60 degrees to the horizontal.
Draw a picture of the object.
Create a right triangle to the horizontal.
Label all known information.
Solve for the x component.
cos ɵ = vx/vi
Solve for the y component.
sin ɵ = vy/vi
40 m/s
60°
cos 60 = vx/40
Vx = 20 m/s
Sin 60 = vy/40
Vy = 34.6 m/s