; 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
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
– 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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