Relative Motion
AP Physics C
Mrs. Coyle
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)
Resultant Velocity
The resultant velocity of an object with respect
to a reference frame is the net velocity
of an object.
vAG = vAB + vBG
Example 1The 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:
a) With respect to the ground?
b) With respect to the bus?
c) 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?
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?
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.
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.
a) What is the resultant velocity of the boat
relative to the shore.
b) How far downstream did the boat travel?
Assume that the river is 300m
wide.
Reference frame S’ is moving with
a constant velocity, vo
Galilean Transformations
Positions as seen from the two
reference frames:
r’ = r – vo t
When you take the derivative:
v’ = v – vo
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.”
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?
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?