1. Kinematics 2 – Projectile Motion

2. Vectors Examples: Represented by arrows
Quantities with magnitude AND direction
Examples:
Represented by arrows
Can be connected together to represent multiple
The sum is called the resultant (shows the overall effect)

3. Adding Vectors
Vectors are (visually) added by connecting the second vector to the tip of the first. C D A B
Show the following combinations
A + B
2B - C
C – D + 2A

4. Vectors Vectors also can be represented two ways
Rectangular: (x, y) form
Polar: (r, θ) form
Sketch the Following
A = (-3, -4)
B = (4, 160o)
C = (2, 75o)

5. Changing Representations
From rectangular to polar
Step 1: Sketch Vector
Step 2: Find magnitude (r) with Pythagorean Theorem
Step 3: Find angle (θ), using =
Step 4: *Angle correction for Quad. II and III
θ =
Example: Convert (-3.0, -8.0)

6. Changing Representations
From polar to rectangular (breaking into components)
Example (4.00, 60.0o)
Example (2.00, 155o)

7. Adding by Components
You are given four vectors:
Vector A (5, 4)
Vector B (-3, 3)
Vector C (1, -4)
Vector D (2, 2)
Sketch the Vector Sum: A + B + C + D and show the resultant You may begin Vector A on the origin.
B. What are the rectangular coordinates of the resultant?
What is the sum of all the x-components of Vectors A through D Ax + Bx + Cx + Dx =
D. What is the sum of all the y-components of Vectors A through D.
Ay + By + Cy + Dy =

8. Adding by Components
To add by components – vectors must be in rectangular form
Find the vector sum:
A ( o) + B (3.00, 225O)

9. Relative Velocity Consider motion from multiple reference frames
If in the same plane, simple addition or subtraction can be used
If not, the resultant vector must be found

10. Example 3
A passenger is seated on a bus traveling 6.0 m/s. If she remains in her seat, what is her velocity with reference to…
The ground?
The bus?
What is her velocity with respect to the ground if she begins to move forward towards the driver with a velocity of 1.0 m/s.

11. Relative Velocity vBS = vBW + vWS
vBW is the velocity of B (boat) with respect to the water
vWS is the velocity of the water (W) with respect to a reference frame (example: the shore)
vBS is the velocity of B with respect to a reference frame (example: the shore)

12. Example 4
A little boat, that can travel at 1.85 m/s in still water (velocity of the boat with respect to the water), heads directly across a river flowing with a current of 1.20 m/s (velocity of the water with respect to the shore). Find the following:
What is the resultant velocity of the boat (both magnitude and direction) (velocity of the boat with respect to the shore).
If the river is m across, how long will it take for him to make it across?