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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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Section 3 8 relative velocity l.jpg

Section 3-8: Relative Velocity


Section 3 8 relative velocity2 l.jpg

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!!


Velocities not along the same line l.jpg

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


Conceptual example 3 10 boat crossing a river l.jpg

Conceptual Example 3-10: Boat Crossing A River

  • vBS = vBW + vWS

  • Outer subscripts on both sides are the same!

  • Inner subscripts are the same!


Can extend this to more than 2 v s l.jpg

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


Example 3 11 l.jpg

Example 3-11


Example 3 12 l.jpg

Example 3-12


Example plane with a cross wind l.jpg

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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