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

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

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

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

Relative velocity in 2-D

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

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

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

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?

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

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

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)