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Section 3-8: Relative Velocity

Section 3-8: Relative Velocity. Section 3-8: Relative Velocity. A useful example of vector addition ! Example: 2 trains approaching each other (along a line) at 95 km/h each, with respect to the Earth.

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Section 3-8: Relative Velocity

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  1. Section 3-8: Relative Velocity

  2. Section 3-8: Relative Velocity • A useful example of vector addition! • Example: 2 trains approaching each other (along a line) at 95 km/h each, with respect to the Earth. • Observers on either train see the other coming at 95 + 95 = 190 km/h. Observer on ground sees  95 km/h.  Velocity depends on reference frame!!

  3. Velocities not along the same line • Need to use full vector addition. • A common error is adding or subtracting wrong velocities • A method to help avoid this is: Proper subscript labeling of velocities • CONVENTION: • Velocities with 2 subscripts. First = object, O, Second = reference frame, R. vOR

  4. Conceptual Example 3-10: Boat Crossing A River • vBS = vBW + vWS • Outer subscripts on both sides are the same! • Inner subscripts are the same!

  5. Can extend this to more than 2 v’s • Suppose, to the previous example, we add a fisherman walking on boat with velocity vFB = velocity of the Fisherman with respect to the Boat: vFS = vFB + vBW + vWS • Outer subscripts on both sides are the same! • Inner subscripts are the same! • Finally: Relative velocities obey: vAB = -vBA

  6. Example 3-11

  7. Example 3-12

  8. Example: Plane with a cross wind vPA = 200 km/h , N vAG = 100 km/h , from NE (to SW) vPG = vPA + vAG Use the rules of analytic addition: Compute components of vPA & vAG Add these to get components of vPG. Compute the length & angle of vPG

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