1. Vectors and motion in 2-D
Adding vectors to find total displacement
Method 1: Graphical addition:
Tail of next vector on tip of previous

2. Method 2: Adding x and y components
Adding vectors to find total displacement
Method 2: Adding x and y components
SP 1.8

3. Method 2: Adding x and y components Add components
Adding vectors to find total displacement
Method 2: Adding x and y components
Add components
Find total’s magnitude from
Find angle from some axis from
SP 1.8

4. A few graphical exercises
P1. Draw A+B, and choose quadrant:
P2. Draw B-A, and choose quadrant
P3. Draw 2A – ½B, and choose quadrant

5. Relative velocity in 2-D

6. If the plane points E, and the wind is S, how will the plane move over the ground?
vPG = vPA + vAG

7. If the vectors aren’t perpendicular… add the components
200
50
vPG = vPA + vAG
vPG = vPA + vAG

8. Math: vPG = vPA + vAG can be written: v­PA = v­PG + - vAG
If the wind is to the S at 90 km/hr, in what direction must a plane flying 500 km/hr airspeed point itself in order to fly exactly E?
Concept: the plane must have part of its v going “upwind” to exactly cancel the effect of the wind; the rest of its v points in the direction you want to go over the ground.
Math: vPG = vPA + vAG can be written: v­PA = v­PG + - vAG
-vAG

9. An ocean has a 10 mph current to the southwest
An ocean has a 10 mph current to the southwest. If a boat wishes to sail at 20 mph north vs the ground (or GPS), what direction should the boat point?

10. HW2: An airplane is flying in a jet stream that is blowing at 45
HW2: An airplane is flying in a jet stream that is blowing at 45.0 m/s in a direction 20º south of east. Its direction of motion relative to the Earth is 45.0º south of west, while its direction of travel relative to the air is 5.00º south of west. Sketch the three vectors and label the known triangle lengths and angles.

11. Lecture 2, HW2 Vectors Basic concepts: Basic problems:
adding two vectors graphically
Basic problems:
adding two perpendicular vectors with Pythagorean them, including for relative velocity
finding components of vectors
finding angle and magnitudes from components
Advanced problems:
adding, subtracting vectors with components
relative velocity with non-perpendicular vectors

12. Concept review
Which of the following graphs represents 1. a bike moving at constant velocity 2. a car speeding up then slowing down 3. a ball thrown up in the air that comes back down 4. a car that always speeds up 5. a motorcycle that slows down and parks. Careful! a, b are velocity v(t), and the others are position x(t)