Vectors in 2 Dimensions 10.0m 6.0m 8.0m

Representation of vectors in 2D Polar form (magnitude and direction) ex: Dr = 10.0m 37⁰ Component form (x and y (and z) components) ex: Dr = (8.0 i + 6.0 j)m or Dr = (8m, 6m) or Dx = 8m, Dy = 6m Graphical form (scale drawing) ex: Dr = 10.0m 37 ⁰

Adding or Subtracting Vectors Vectors can only be added or subtracted if they are in COMPONENT or GRAPHICAL forms ADDING Graphically: Make a scale drawing ADDING or SUBTRACTING by components: Convert vectors from polar to component form Add or subtract x comp., add or subtract y comp. Convert back to polar form (if needed)

Converting Vectors: Polar to Comp. Sketch the polar vector Sketch the components (legs) X, then Y Use trig to compute the components Repeat as needed for other vectors Ex: Convert 20m, 120 ⁰ to component form

Converting Vectors: Comp. to Polar Draw the X then Y components (legs) TIP to TAIL Draw the hypotenuse (magnitude of polar vector) Compute the direction of the polar vector Ex: Convert Dr = -15.00m i - 17.32m j (Dx = -15.00m Dy = - 17.32m) to polar form

Converting Practice Convert 20m, 120° to component form. Convert Dr = (-15 i + -17.3 j)m to polar form.

Position & Displacement in 2D Dr = rf-ri where rf and ri are position vectors Drtotal = Dr1 + Dr2+…+ Drn r = xî + yĵ + zǩ

Examples Ex1: During practice, Ryan marches 10m,30° and then 10m, 150°. What is his total displacement? Ex2: A radar station tracks a satellite that moves from 160km,28° to 100 km70°. What is the satellite’s displacement?

Posted Examples p 57 # 5, 8, 11, 16, 15