1. Vectors
Day 7
Lyzinski Physics

2. Day #7

3. A man is standing on a riverboat next to his wife
A man is standing on a riverboat next to his wife. The boat is moving down a river without propelling itself, using only the current’s speed, which is 50 ft/min. The man starts jogging towards the front of the boat with a speed of 100 ft/min. During his jog, a smaller boat, traveling at 150 ft/min (relative to the water), passes the boat (in the same direction). A bird is sitting on the shore, watching the whole situation unravel.
150 ft/min 
What is the man’s velocity (relative to the bird) when he is running?
What is the man’s velocity (relative to his wife) when he is running?
What is the man’s velocity (relative to the speedboat) when he is running?
What is the wife’s velocity relative to the bird?
What is the wife’s velocity relative to the speedboat?
100 ft/min 
50 ft/min 
50 ft/min 
150 ft/min 

4. It depends on the “Frame of Reference” of the observer.
So, what was the velocity of the man? It depends. What is the velocity relative to?
It depends on the “Frame of Reference” of the observer.

5. Two cars are moving towards each other on a highway
Two cars are moving towards each other on a highway. Car A moves East at 60 mph, while car B moves West at 50 mph. Find the velocity of car A with respect to … a) car B b) a bird sitting on the side of the highway c) a boy in the backseat of car A
110 mph [E]
60 mph [E]
0 mph
V AG = 60 mph
V BG = 50 mph

6. In relative velocity problems, we often use what is known as a “relative velocity equation”.
When you see a term like “VBC” this means “the velocity of the Ball relative to the Car”
(for example)

7. The relative velocity equation
vBS = vBC + vCS
Here’s an easy trick to remember the equation
vBS =
vBS vB
vBS +
v S C C
VBS = velocity of the ball relative to the side of the road
VBC = velocity of the ball relative to the car
VCS = velocity of the car relative to the side of the road

8. * REALLY IMPORTANT NOTE

9. VAB = VAG + VGB = + VAbird = VAG + VGbird = + VAboy = VAG + VGboy = +
Looking at this problem again 
Two cars are moving towards each other on a highway. Car A moves East at 60 mph, while car B moves West at 50 mph. Find the velocity of car A with respect to … a) car B b) a bird sitting on the side of the highway c) a boy in the backseat of car A
VAB = VAG + VGB =
60 mph mph
110 mph [E]
60 mph [E]
VAbird = VAG + VGbird =
60 mph
0 mph
VAboy = VAG + VGboy =
60 mph mph

10. vBS = vBC + vCS vBS = vBC + vCS
Example: A boy sits in his car with a tennis ball. The car is moving at a speed of 20 mph. If he can throw the ball 30 mph, find the speed with which he will could hit…
his brother in the front seat of the car.
b) A sign on the side of the road that the car is about to pass.
c) A sign on the side of the road that the car has already passed
30 mph
50 mph
vBS = vBC + vCS
30 mph
20 mph
10 mph
20 mph
vBS = vBC + vCS
30 mph

11. River Problems

12. River Problems vCB = vCW + vWB
Crossing a river: aiming straight across, but not accounting for the moving water 
VCW = velocity of the canoe relative to the water
(the velocity that the canoeist paddles)
VWB = velocity of the water relative to the riverbank
(the velocity of the river current)
VCB = velocity of the canoeist relative to the riverbank
vCB = vCW + vWB

13. VCW = velocity of the canoe relative to the water
(the velocity that the canoeist paddles)
VWB = velocity of the water relative to the riverbank
(the velocity of the river current)
VCB = velocity of the canoeist relative to the riverbank
When answering any questions about going “ACROSS” the river, use the ACROSS THE RIVER Component.
When answering any questions about going “DOWNSTREAM, use the DOWNSTREAM Component.
The “slanted” vector is how the canoe will move from the perspective of anyone standing on the shore.

14. Example: A 20 m wide river flows at 1. 5 m/s
Example: A 20 m wide river flows at 1.5 m/s. A boy canoes across it at 2 m/s relative to the water. a. What is the least time she requires to cross the river? b. How far downstream will she be when she lands on the opposite shore? c. What will her velocity relative to the shore be as she crosses?
d = rt  20m = (2 m/s) t  t = 10 seconds.
d = rt = (1.5 m/s)(10 sec) = 15 meters 2
1.5
2.5
2.5 m/s [across 36.87o downstream]

15. River Problems vGB = vGW + vWB
Crossing a river: trying to go from point A to point B B
VWB = velocity of the water relative to the riverbank
(the velocity of the river current)
VGB = velocity of the girl relative to the riverbank
VGW = velocity of the girl relative to the water
(the velocity that the girl swims) A
vGB = vGW + vWB

16. Example: A river is 20 m wide. It flows at 1. 5 m/s
Example: A river is 20 m wide. It flows at 1.5 m/s. If a girl swims at a speed of 2 m/s, find: a) the time required for the girl to swim 15 m upstream. b) the time required for the girl to swim 15 m downstream. c) the angle (between the swimmers path and the shore that the girl should aim when crossing the river if she wants to arrive at the other side directly across from her starting point.
d = rt  15m = (2 m/s – 1.5 m/s)t  t = 30 seconds
d = rt  15m = (2 m/s m/s)t  t = 4.29 seconds 2
1.5
1.32 q q
q = cos-1 (1.5/2) = 41.4o
[upstream 41.4o across]

17. From previous example: A river is 20 m wide. It flows at 1. 5 m/s
From previous example: A river is 20 m wide. It flows at 1.5 m/s. The girl swims at a speed of 2 m/s. d) How long will it take to cross the river in this case (the case where the girl adjusts for the current by pointing herself upstream)
d = rt  20m = (1.32 m/s)t  t = 15.2 seconds 2
1.5
1.32 q

18. “Day #7 Vectors HW Problems” (from the packet)
Tonight’s HW
“Day #7 Vectors HW Problems” (from the packet)
#’s 36-44