CH1 – Kinematics – FRAMES OF REFERENCE & RELATIVE VELOCITY
Course/Section: SPH 4U
Date: _ _______
Lesson Big Idea: Motion is observed/explained relative to a specified frame of reference (FOR) – specifically
‘relative velocity’ is an object’s velocity relative to a specified object.
Ministry Expectations:
B3.1 distinguish between reference systems (inertial and non-inertial) with respect to the real and apparent
forces acting within such systems (e.g., apparent force in a rotating frame, apparent gravitational force in a
vertically accelerating frame, real force pulling on the elastic of a ball-and-paddle toy).
Learning Goals:
Success Criteria:
 Understanding what a FOR is, how to choose I will know my students have attained these learning goals
if given a random relative velocity problem, they are able
one
to identify the problem’s variables and associated
 How to construct, manipulate and draw a
subscripts, and be able to conceptually understand why we
representational diagram for relative velocity
are adding 2 velocities to get a resultant velocity
equations
Before: Minds On
Time
:
Description
Airplanes
Boats
Even if a plane flies directly to its
destination at constant speed, why
might it arrive late?
As a visual aid, check out this plane
Landing in high winds:
Why is it so difficult to
paddle across a river?
Check out these extreme
river currents as a visual
aid:http://www.youtube.com/
http://www.youtube.com/watch?v=
mMvLuUJFHYk
Assessment
Materials
Projector,
screen,
speakers –
show video
of airplane
experiencing
turbulence.
Show video
of boaters
paddling
across river.
watch?v=r2kZGyEEcts&list=P
L565E734945AEB0F5
Transition from Minds On to Action:
-In the case of the plane, wind turbulence causes the plane to veer off course in a different direction –
the plane must compensate for this in order to re-navigate it, resulting in lost time.
-In the case of paddling across a river, it might seem like a short distance, but river currents will push
you down the river, not across it, so as you fight the current to go straight, you are actually going on an
angle.
During: Action
Time
:
Description
1. Def’n – Frame of Reference (FOR): A coordinate system relative
to which motion is observed/measured.
- we are used to using the ground or other stationary objects as FOR’s
- can use moving objects too, just not accelerating ones (covered later)
2. Def’n – Relative Velocity: The velocity of an object
observed/measured relative to specified FOR.
3a. Airplane Example Revisited
P – Plane; E – Earth; A – Air
vPE – velocity of Plane relative to
Earth (e.g. resulting velocity)
vPA – velocity of Plane relative to
the Air (e.g. Plane’s speed without
wind, say 500 km/h)
vAE – velocity of Air relative to
Earth (e.g. windspeed, say 70
km/h)
3b. Relative Velocity Equation
In order to determine the plane’s resultant velocity (i.e. the plane’s
velocity with no wind – vPA plus the air velocity – vAE the windspeed),
we add the 2 vectors:
*NOTICE: the equation must
always be written such that the
vPE = vPA + vAE
centre subscripts (in this case,
“A”) when ignored, leave the
resultant’s subscripts (“PE”).
3c. Calculate Plane’s Velocity Relative to the Earth:
A Plane is flying from New York to Hong Kong – with no wind, the
plane reaches a speed of 500 km/h [E]. However, wind turbulence
caused by 70 km/h [W] winds is slowing the plane down. What is it’s
resultant velocity?
vPA= 500 km/h [E]
vAE = 70 km/h [W] ≡ -70 km/h [E]
vPE = vPA + vAE
= 500 km/h [E] + (-70 km/h [E])
= 430 km/h [E]
Therefore with these high winds, the plane’s velocity has been reduced
to 430 km/h [E].
Assessment
Materials
Blackboard
4a. Boat Example Revisited B – Boat; S – Shore; W – Water
vBS – velocity of Boat relative to Shore
(e.g. resulting velocity)
vBW – velocity of Boat relative to the
Water (e.g. Boat’s velocity in still water,
say 5 m/s [N])
vWS – velocity of Water relative to Shore
(e.g. water current velocity, say 3 m/s [E])
4b. Whiteboard Activity – Expanding on 3c.
Your cousin is teaching you how to boat across a fast moving, 220 m
wide river, while you stand on the shore. He paddles north across the
river at 5 m/s, while the strong water currents flow east at 3m/s. What
is his velocity relative to you?
3m/s
5m/s
θ
a
N
vB-you = vBS = ?
vBW = 5m/s [N]; vWS = 3m/s [E]
*Make sure centre subscripts cancel*
vBS = vBW + vWS
= 5m/s [N] + 3m/s [E] = √52 + 32
≈ 5.83 m/s [N θo E]
Direction:
3
tanθ = 5; θ ≈ 31o
Therefore your cousin’s velocity relative
to you is 5.83 m/s [N 31o E].
This is similar
to the plane
question, but
these relative
velocities are
at an angle,
not just backand-forth.
Whiteboards
, whiteboard
markers,
tissues for
erasing.
Consolidation
Time
:
Description
1. Frame of Reference (FOR): A coordinate system relative to which
motion is observed/explained.
2. Relative Velocity: velocity of an object relative to a specified frame
of reference.
3. Manipulate Relative Velocity Equation(s): vAB + vBC = vAC
4. Always remember to include a direction, including angle,
navigation (N, E, S, W, up, down)
Assessment
Materials
Assign
Relevant
Textbook
Problems