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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 velocity2
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
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
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
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 plane with a cross wind
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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