# Section 3-8: Relative Velocity - PowerPoint PPT Presentation

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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

• 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

• 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

• 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

• 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

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