Relative Motion
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:
Boat Crossing A River
• 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
Example
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