Velocity Problems

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Velocity Problems

• GE 111 - Lecture 7

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How do you solve problems?

• In essence ask yourself
• What is the purpose of this problem?
• What do I need to know to solve the problem?
• What resources do I have at my disposal?
• How do I get from what I have, to what I need to
  know?
• Exploration may be required
• Learning to see paths to a solution requires
  practice, persistence, and pain (unfortunately).
• Problem solving is not learned by copying others
  work all problems are different.

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Remember

• When problem solving, remember .
• Significant Figures (How sure are you?)
• Use a reasonable number of sig. figs!
• Units
• Always give the units of your answers
• Use appropriate units (km/h vs.
  furlong/fortnight)
• Verification
• Ask yourself, Does this answer make sense?
• Recognize the sizes of things (Wee or not so
  wee?)
• CONFIRM THAT YOU ANSWERED THE QUESTION BEING
  ASKED!!!

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Distance/Velocity/Time

• Types of Distance/Velocity/Time questions
• Simple d v t
• Multi-stage
• Destination / Return
• Circular track
• Opposing
• Lapping

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Average Velocity

• NOT found by averaging velocities!
• Must use Total distance / Total time
• A car travels along a straight highway for 1.0
  hour at 100km/h and 15 min at 50 km/h. What is
  the average velocity?
• Vave (100km/h50km/h)/2 75km/h
• Vave ((100km/h)1h(50km)0.25h)/1.25h
  90km/h

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Area Under the Curve

• Distance - the integration of velocity over time
  (area under velocity vs. time graph)
• Can be helpful to sketch
• In this case, area under both curves is equal

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Velocity Problem 1

• An airplane flies with a velocity of 250 mph when
  there is no wind. In flying with the wind, it
  travels a certain distance in 4h. However, in
  flying against the wind, it can travel only 60
  percent of that distance. What is the winds
  velocity?

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Velocity Problem 2

• A student is driving home, a distance of 150 mi,
  for the weekend. From previous experience, the
  student knows that increasing the average speed
  by 10 mi/h could reduce the time of the trip by
  35 min. What is the actual average speed?

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Velocity Problem 3 (A Past Exam Question)

• Peter runs from home to the University at an
  average speed of 15 km/hr and returns by the same
  route at an average speed of 12 km/hr. The total
  time to and from work was 72 mins. How far is it
  from Peters home to the University?

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Velocity Vectors

• Compensating for wind or current
• Resultant velocity in wind or current
• Sometimes involves working with both velocity and
  distance diagrams, and being careful that youre
  using the right one!

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Velocity Vector Example 1

• A canoeist can paddle twice as fast as the
  current in a river. At what angle upstream must
  the canoeist head in order to paddle straight
  across the river?For velocity vector questions,
  be sure to sketch a diagram!

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V.V. Example 1(continued)

• Since the canoe travels straight across, the
  resulting triangle must be a right triangle
• Use sin? x/2x ½ to solve ?
• ? 30

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V.V. Problem 1 (A past midterm question)

• A small aircraft has a flying speed of 200 km/h
  in still air.
• To make a trip from Saskatoon to Regina, a
  straight line distance on the map of 250 km, a
  pilot must first determine the wind velocity and
  then calculate what direction to fly (the
  'heading') to compensate for the wind.  (NOTE 
  All headings are referenced from the North,
  measured positive in the clockwise direction, eg.
  East is 90 degrees)
• Assume Regina has a heading on the map of 150
  degrees from Saskatoon, and that the wind is
  blowing steady from North to South.  The pilot
  determines that the aircraft heading must be 140
  degrees in order to end up in Regina. 
• a) What is the wind speed?
• b) How long will it take to make the trip from
  Saskatoon to Regina?

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V.V. Problem 2 (A past Final Exam question)

• A boat capable of traveling 5 km/hr in still
  water is used to cross a river that is 1 km wide.
  The water in the river is flowing at 2 km/hr
  towards the east. If the boat starts on the
  south shore and needs to follow a straight line
  path to a dock on the north shore, 2 km to the
  east
• a) What heading must the boat travel? (Heading is
  defined as the number of degrees east of north)
• b) How long will the trip take?