; Ch. 3-4 Relative Motion
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Ch. 3-4 Relative Motion

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									Chapter 3–4:
Relative Motion




      Physics
      Coach Kelsoe
      Pages 102–105
          Objectives

• Describe situations in terms of frame of
  reference.
• Solve problems involving relative velocity.
          Frames of Reference

• If you are moving at 80 km/hr north and a car
  passes you going 90 km/hr, to you the faster
  car seems to be moving north at 10 km/hr.
• Someone standing on the side of the road
  would measure the velocity of the faster car
  as 90 km/hr toward the north.
• This simple example demonstrates that
  velocity measurements depend on the frame
  of reference of the observer.
            Frames of Reference
•   Consider a stunt dummy dropped from a
    plane.
    a) When viewed from the plane, the stunt dummy
       falls straight down.
    b) When viewed from a stationary position on the
       ground, the stunt dummy follows a parabolic
       projectile path.
               Relative Velocity
• When solving relative velocity problems, write down
  the information in the form of velocities with
  subscripts.
• Using our earlier example, we have:
   – vse = +80 km/hr north (se = slower car with respect to
     Earth)
   – vfe = +90 km/hr north (fe = faster car with respect to Earth)
   – unknown = vfs (fs = fast car with respect to slow)
• Write an equation for vfs in terms of the other
  velocities. The subscripts start with f and end with s.
  The other subscripts start with the letter that ended
  the preceding velocity:
   – vfs = vfe + ves
              Relative Velocity
• An observer in the slow car perceives Earth as
  moving south at a velocity of 80 km/hr while a
  stationary observer on the ground (Earth) views the
  car as moving north at a velocity of 80 km/hr. In
  equation form:
   – ves = -vse
• Thus, this problem can be solved as follows:
   – vfs = vfe + ves = vfe – vse
   – vfs = (+90 km/hr n) – (+80 km/hr n) = +10 km/hr n
• A general form of the relative velocity equation is:
   – vac = vab + vbc
           Sample Problem

• Relative Velocity
  A boat heading north crosses a wide river with
  a velocity of 10.00 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.
             Sample Problem Solution

• Set up your coordinate system with
  your givens.
  – Given:
    • vbw = 10.00 km/hr due north (velocity of
      the boat, b, with respect to the water, w)
    • vwe = 5.00 km/hr due east (velocity of the
      water, w, with respect to the Earth, e)          vwe
  – Unknown:
    • vbe = ?
                                            vbw          vbe
  – Diagram:
                                                   θ
    • See diagram
            Sample Problem Solution

• Choose an equation or situation:
  – vbe = vbw + vwe
  – (vbe)2 = (vbw)2 + (vwe)2
  – tan θ = vwe /vbw
• Rearrange the equations to isolate the
  unknowns:
  – vbe = √(vbw)2 + (vwe)2
  – θ = tan-1 vwe /vbw
           Sample Problem Solution

• Substitute the known values into the
  equations and solve.
  – vbe = √(10.00 km/hr)2 + (5.00 km/hr)2
  – vbe = 11.18 km/hr
  – θ = tan-1 (5.00 km/hr /10.00 km/hr)
  – θ = 26.6° east of north

								
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