Constant Acceleration and Relative Velocity

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Constant Acceleration and Relative
Velocity
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Relative Velocity

• Sometimes your velocity is known relative to a
  reference frame that is moving relative to the
  earth.
• Example 1 A person moving relative to a train,
  which is moving relative to the ground.
• Example 2 a plane moving relative to air, which
  is then moving relative to the ground.
• These velocities are related by vector addition

• vac is the velocity of the object relative to the
  ground
• vab is the velocity of the object relative to a
  moving reference frame
• vbc is the velocity of the moving reference frame
  relative to the ground

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Relative Velocity

• You are on a train traveling 40 mph North. If you
  walk 5 mph toward the front of the train, what is
  your speed relative to the ground?
• A) 45 mph B) 40 mph C) 35 mph

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Relative Velocity

• You are on a train traveling 40 mph North. If you
  walk 5 mph toward the rear of the train, what is
  your speed relative to the ground?
• A) 45 mph B) 40 mph C) 35 mph

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Relative Velocity

• You are on a train traveling 40 mph North. If you
  walk 5 mph sideways across the car, what is your
  speed relative to the ground?
• A) lt 40 mph B) 40 mph C) gt40 mph

40 mph N 5 mph W
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Example airplane

• An airplane needs to fly due south to reach its
  destination, but there is a wind blowing from the
  east. Will this increase, decrease or have no
  effect on the travel time?

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Example

• Three swimmers can swim equally fast relative to
  the water. They have a race to see who can swim
  across a river in the least time. Relative to
  the water, Beth (B) swims perpendicular to the
  flow, Ann (A) swims upstream, and Carly (C) swims
  downstream. Which swimmer wins the race?
• A) Ann
• B) Beth
• C) Carly

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Think of a swimming pool on a cruise ship
When swimming to the other side of the pool, you
dont worry about the motion of the ship !
A B C
HW swimmer
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Example

• If the width of the river is 50m and Beth can
  swim at 3m/s, how long does it take her to get
  across? If the river is flowing at 2m/s, How far
  downstream is she swept?

2m/s
50m
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Swimmer Example

• What angle should Ann take to get directly to the
  other side if she can swim 3 mph relative to the
  water, and the river is flowing at 2 mph?How
  long does it take her to get across?

2m/s
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Summary of Concepts

• X and Y directions are Independent!
• Position, velocity and acceleration are vectors
• F m a applies in both x and y direction
• Relative Motion (Add vector components)