1. Chapter 2 : Kinematics in Two Directions
2.3 Velocity Vectors &
Relative Motion

2. Relative Motion 1-D Relative Motion
Using different frames of reference
1-D Relative Motion
Me on truck?
Person on sidewalk?
Scenario 1: Throwing apples forward at 15 m/s out of a motionless truck
Scenario 2: Throwing apples at 15m/s forward while the truck moves 20 m/s forward.
Scenario 3: Turn around and start throwing apples 15 m/s backward while the truck moves 20 m/s forward.
Me on truck?
Person on sidewalk?
Me on truck?
Person on sidewalk?

3. Relative Velocity
Scenario 4: Sitting at your desk, how fast are you moving?
Relative to the ground: 0 m/s
Relative to the sun: 2.97 x 104 m/s

4. 2-D Relative Motion
Confusion arises when an object is moving relative to a frame of reference that is also in motion.
Birds or planes flying in windy conditions
Swimmers or boats crossing moving water in a river

5. 50km/h [W] + 40 km/h [E] = 10 km/h [W] b) EAST?
Example 1: A bird flies at 50 km/h in an area where a WEST wind of 40 km/h is blowing. What is the resultant velocity of the bird when it flies…
WEST?
50km/h [W] + 40 km/h [E] = 10 km/h [W]
b) EAST?
50km/h [E] + 40 km/h [E] =
90 km/h [E]
NOTE: Winds blow from someplace, thus a WEST wind is coming from the west and is heading EAST

6. c) NORTH? d) 60o [North of West]

7. Example 2: An airplane flies NORTH at
300 km/h but an EAST wind is blowing at 70 km/h.
What is the actual velocity of the plane?
How far off the original course will the plane be after 3 h?

8. Example 3: City A is 600 km SOUTH of City B
Example 3: City A is 600 km SOUTH of City B. An airplane which can fly at a 200 km/h must fly from City B to City A. A WEST wind of 90 km/h is blowing.
What is the required heading?
b) What is the actual velocity of the plane relative to the ground?
c) How long is the flight from City B to City A?

9. Example 4: A girl standing on the WEST side of a river that flows from NORTH to SOUTH at 1.5km/h wishes to swim straight across the river. She can swim at 3 km/h in still water.
What is the heading she must use?
What is her actual velocity?
If the river is 0.25 km wide, how long would it take her to swim across the river, in minutes?

10. bVw = velocity of boat in still water
Example 5: You are in a boat that can move in still water at 7.0 m/s. You point your boat directly EAST across a river to get to the other side that is 200 m away. The river is flowing at 4.0 m/s [N].
a) Determine your velocity measured by someone on the shore
bVw = velocity of boat in still water
wVs = velocity of the water with respect to shore
bVs = velocity of boat with respect to shore
bVs
wVs
bVw

11. Example 4: You are in a boat that can move in still water at 7. 0 m/s
Example 4: You are in a boat that can move in still water at 7.0 m/s. You point your boat directly EAST across a river to get to the other side that is 200 m away. The river is flowing at 4.0 m/s [N].
a) Determine your velocity measured by someone on the shore
4.0 m/s x
7.0 m/s

12. v = d t How far does the boat need to travel? 200 m
Example 4: You are in a boat that can move in still water at 7.0 m/s. You point your boat directly EAST across a river to get to the other side that is 200 m away. The river is flowing at 4.0 m/s [N].
b) Determine how much time it takes for the boat to cross the river.
How far does the boat need to travel?
200 m
How fast is the boat travelling?
7.0 m/s
v = d t

13. Example 4: You are in a boat that can move in still water at 7. 0 m/s
Example 4: You are in a boat that can move in still water at 7.0 m/s. You point your boat directly EAST across a river to get to the other side that is 200 m away. The river is flowing at 4.0 m/s [N].
C ) Determine how far downstream from directly across the river the boat will hit the shore.
wVs is pushing the boat downstream.
Use the time you just calculated
v = d t