1. What do you think?
One person says a car is traveling at 10 km/h while another states it is traveling at 90 km/h. Both of them are correct. How can this be?

2. Chapter 3
Relative Motion

3. Relative Velocity
Relative velocity is about relating the measurements of two different observers
It may be useful to use a moving frame of reference instead of a stationary one
It is important to specify the frame of reference, since the motion may be different in different frames of reference
There are no specific equations to learn to solve relative velocity problems

4. Relative Velocity
(See Page 102)

5. Relative Velocity Notation
The pattern of subscripts can be useful in solving relative velocity problems
Assume the following notation:
E is an observer, stationary with respect to the earth
A and B are two moving cars

6. Relative Position Equations
is the position of car A as “viewed” by E
is the position of car B as “viewed” by E
is the position of car A as viewed from car B

7. Relative Position
The position of car A relative to car B is given by the vector subtraction equation

8. Relative Velocity Equations
The rate of change of the displacements gives the relationship for the velocities

9. So, now what do you think?
One person says a car is traveling at 10 km/h while another states it is traveling at 90 km/h. Both of them are correct. How can this be?

10. Problem-Solving Strategy: Relative Velocity
Label all the objects with a descriptive letter
Look for phrases such as “velocity of A relative to B”
Write the velocity variables with appropriate notation
If there is something not explicitly noted as being relative to something else, it is probably relative to the earth

11. Problem-Solving Strategy: Relative Velocity, cont
Take the velocities and put them into an equation
Keep the subscripts in an order analogous to the standard equation
Solve for the unknown(s)
Use vector addition or subtraction

12. In-Class Exercise (ICE)
A boat is traveling upstream. The speed of the boat with respect to Earth is 20 km/h. The speed of the river with respect to Earth is 5 km/h. What is the speed of the boat with respect to the river?
25 km/h

13. Example
A boat heading north crosses a wide river with a velocity of km/hr relative to the water. The river has a uniform velocity of 5.00 km/hr due east. Determine the boat’s velocity with respect to an observer on shore.

14. In-Class Exercise (ICE)
A plane flies northeast at an airspeed of 563 km/h. (Airspeed is the speed of the aircraft relative to the air.) A 48.0 km/h wind is blowing to the southeast. What is the plane’s velocity relative to the ground?
565.0 km/h at 40.1° north of east

15. In-Class Exercise
A passenger jet is traveling at a speed of 735 km/h at a direction of 35.0o south of west. A Cessna-172 is traveling at a speed of 215 km/h at a direction of 25.0o east of south. What is the velocity of the jet with respect to the Cessna?
729 km/h at 65.2° ahead and right

16.  = 35.0o 215 km/h 735 km/h  = 25.0o Vector x-component y-componentCE
215 km/h·sin25.0o = 91 km/h
-215 km/h·cos25.0o= -195 km/h JE
-735 km/h·cos35.0o = -602 km/h
-735 km/h·sin35.0o= -422 km/h
JE-CE=JC
693 km/h
227 km/h