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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.

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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.

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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.

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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).

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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.

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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.

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“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.

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