1. Chapter 3 Projectile Motion
Conceptual Physics
Hewitt, 1999

2. 3.1 Vector & Scalar Quantities
Vector- magnitude and direction (23m/s N)
Only units that can have direction can be vectors
Velocity (speedometer & compass)
Scalar- magnitude only (23m/s, 34°C, 56s, 3L, 85kg)
Some units simply can’t have direction, like time and temperature
Speed (speedometer only)

3. 3.2 Velocity Vectors We use an arrow to represent velocity vectors
Arrow shows direction, length shows relative magnitude
We can then add, subtract or use other math to find the sum of all of the vectors
If drawn correctly, we can just use a ruler!
Draw to an appropriate scale (1cm=10m/s?)
Using simple trigonometry (remember a2+b2=c2?), we can find the sum of non-linear vectors

4. Vector Addition
By placing vectors tail-to-tip, we can line them up to add them!

5. Rectangle & Vectors
A rectangle (or a right triangle) helps us resolve vectors
Diagonal (or hypotenuse) is the resultant
Parallelogram can be used of the rectangle doesn’t have 90° angles
Special Angles
3,4,5 triangle- angle between 4 & 5 is 37.5°
1,1,√2 triangle- angle between 1 & √2 is 45°
Gives the maximum range (or distance) when launching/throwing

6. Example Problem
If I row my boat north at 80m/s and am caught in a east cross current of 60m/s, what is my actual velocity?
= c2
√( ) = 100m/s
This is a 3,4,5 triangle, so our angle is 37.5°
Magnitude and direction
Direction is stated as 37.5° from some reference line (usually the horizontal or vertical)
Final answer: 100m/s 37.5° East of North

7. 3.3 Components of Vectors
Component- a pair of vectors that can describe a single vector
Vertical and Horizontal components
Resolution- the process of breaking down a vector into its components

8. 3.4 Projectile Motion
Projectiles-Anything that moves vertically (due to earth’s gravity) and horizontally (independent of g)
Dimensional independence- Horizontal motion is independent of gravity

9. 3.5 Upwardly Launched Projectiles
If the object followed a straight line, then the vertical distance beneath the line would be the distance that the ball would have fallen if dropped from that height
Remember d= ½gt2?
Velocity up is opposite of velocity down at the same elevation
Always ignoring air resistance
Would slow down the projectile
Figure 3.15

10. Projectile Resolution

11. Projectile Resolution
Look at the horizontal components. Do they ever change? What does that tell you?
Look at the vertical velocity components for the same height. They should be the same, just in opposite directions. What does this say about velocity?
These paths ignore air resistance. What would the path actually look like if air resistance was added? Would the object go farther/higher or shorter/lower?

12. 3.6 Fast-Moving Projectiles- Satellites
Satellite- an object that is really falling toward the earth as fast as the earth is moving away from it
If you throw a ping-pong ball, it won’t go very far.
If you throw a baseball very fast; it will travel very far.
What about shooting a bullet? It travels even farther.
“Falls” above the atmosphere to avoid air resistance
A rocket can “throw” itself fast enough to travel to the end of the earth, but then the earth has moved, so it keeps falling…

13. Satellite Motion

14. Homework & Assessments
Review Questions 1-18
Plug & Chug 1-10
Think & Explain 1-4
Chapter 2-3 Exam