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. 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

3. Method 2: Adding x and y components
Adding vectors to find total displacement
Method 2: Adding x and y components
PHET

4. 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

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. An airplane is flying in a jet stream that is blowing at 100 m/s in a direction 20º south of east. Its direction of motion relative to the Earth is 45.0º south of west at 200 m/s. Find the heading direction and airspeed of the airplane. Sketch the three vectors as a vector sum or difference e.g. vPG = vPA + vAG or vPA = vPG - vAG Label the vectors vPG , vPA , vAG

11. Lecture 2, HW2 Vectors Basic concepts: Basic problems:
adding two vectors graphically
Basic problems:
adding two perpendicular vectors with Pythagorean theorem for displacement and 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)