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:
  • Understanding what a FOR is, how to choose one
  • How to construct, manipulate and draw a representational diagram for relative velocity equations
/ Success Criteria:
I will know my students have attained these learning goals if given a random relative velocity problem, they are able to identify the problem’s variables and associated subscripts, and be able to conceptually understand why we are adding 2 velocities to get a resultant velocity

Before: Minds On

Time: / Description / Assessment / Materials
Airplanes

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:

mMvLuUJFHYk / Projector, screen, speakers – show video of airplane experiencing turbulence.
Show video of boaters paddling across river.
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 / Assessment / Materials
/ 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
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:

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’sresultant 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].
4a. Boat Example Revisited

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?






/ Blackboard

Consolidation

Time
: / Description / Assessment / Materials
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) / Assign Relevant Textbook Problems