1. Navigation and Relative Velocity  Navigation: how to arrive where you want to go while considering the factors affecting your motion (wind, currents, speed without wind or current, etc.)  Relative velocity: velocity of one object from the point of view (frame of reference) of another object.

2. Navigation  Be clear on what affects the overall motion of the object:  Boats are affected by water current, a motor, and wind. The sum of these vectors will give a resultant of the overall motion or “the motion relative to a stationary observer.”  Planes are affected by wind speed air speed. The sum of these will give the ground speed of the plane.

3. Two Methods (navigation)  ONE: resolve all vectors into components and make two problems out of the two directions of motion (add all East/West vectors together; add all North/South vectors together).  Use a right triangle to find the resultant motion.  TWO: add each contributing vector to the other in a triangle (arrows tip to tail).  Use the cosine law and sine law to find the magnitude and direction of the resultant.

4. Relative Velocity  When two objects move, three obvious perspectives can be considered…they are each very different from each other.  Example: Object A moves north at 20 m/s on a collision course with object B moving at 20 m/s south (that’s our external perspective).

5.  In the frame of reference of object A, it is stationary, while object B is moving south at 40 m/s.  In the frame of reference of object B, the opposite is true.  What about the frame of reference of an observer located 100 m west from a point mid-way between the two objects? Very different perspectives.

6. Suggestions for Success  Geometry: attention to detail when drawing and labeling angles…never assume 90º, or parallel with the x or y axis.  Poor diagrams cause confusion, use a ruler; draw a reasonable size.  Memorized processes get in the way of understanding. Navigation solutions can be estimated easily if the problem is thought out in advance.  Imagine the problem from more than one perspective to gain more under- standing.

7. “It’s Fine When YOU Do It!”  Have you REPEATED examples from class and from the text?  How many problems have you completed on your own?  How quickly do you ask for assistance when you don’t understand in class? (same day? Next day? Or…um…er..NEXT WEEK?  Address your issues with these questions and your goals are well within your grasp.