1. Relative Motion
AP Physics C Mrs. Coyle

2. Relative Velocity Velocity of A relative to B: VAB= VAG - VBG
vAB is the velocity of A with respect to B
vBG is the velocity of B with respect to a reference frame (example: the ground)
vAG is the velocity of A with respect to a
reference frame (example: the ground)

3. Resultant Velocity
The resultant velocity of an object with respect to a reference frame is the net velocity
of an object.
vAG = vAB + vBG

4. Example 1- The Bus Ride
A passenger is seated on a bus that is traveling with a velocity of 6 m/s, E.
If the passenger remains in her seat, what is her velocity:
With respect to the ground?
With respect to the bus?
The passenger decides to approach the driver with a velocity of 1 m/s. What is the velocity of the passenger with respect to the ground?

6. Example 2- Airplane and Wind
An airplane has a velocity of 60 m/s, N with respect to the wind. It is facing a headwind of 5m/s with respect to the ground.
What is the resultant velocity of the airplane with respect to the ground?

7. Example 3-Airplane and Wind
An airplane is traveling with a velocity of 80 m/s, E with respect to the wind. The wind is blowing with a velocity of 4 m/s, S. Find the resultant velocity of the plane with respect to the ground.

8. Example 4- Boat and River
A boat is has a velocity of 8 m/s, E in still water. It is in a river that has a velocity of 3 m/s, S.
What is the resultant velocity of the boat relative to the shore.
How far downstream did the boat travel? Assume that the river is 300m
wide.

10. Reference frame S’ is moving with a constant velocity, vo

11. Galilean Transformations
Positions as seen from the two reference frames:
r’ = r – vo t
When you take the derivative:
v’ = v – vo

12. Acceleration
“The acceleration of the particle measured by an observer in one reference frame is the same as that measured by any other observer moving at a constant velocity relative to the first frame.”

13. Example- 5 (Q #28)
A passenger on a train that is moving with constant velocity drops a spoon. What is the acceleration of the spoon relative a) to the train and b) the Earth?

14. Example 6 (Q#26)
A sailor drops a wrench from the top of a sailboat while the boat is moving rapidly and steadily in a straight line. Where will the wrench hit the deck?