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 = 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