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Objectives Quiz 3
• Determine graphically the sum of two or more vectors
• Solve problems of relative velocity
• Establish a coordinate system in problems involving vector quantities
• Use the process of resolution of vectors to find the components of vectors
Objectives Quiz 3
• Determine algebraically the sum of two or more vectors by adding the components of the vectors
Graphical Vector Addition
• ------------------ + ------ = ----------
• --- + --- = --------
• ------------------------------------ + =
--------------------------------What could each of these represent?
Relative Velocity
• Using vector addition to arrive at actual speed– How fast compared to what?
• A plane can fly at 300 mph with no wind relative to the ground. What is the planes relative velocity when– Has a tail wind of 30 mph?– Has a head wind of 50 mph?
Relative Velocity
• A boy can swim at 3.5 m/s in calm water. The boy goes swimming in a river with a current of 1.5 m/s.
• If the boy swims upstream, how fast does he move relative to shore?– How fast is the boy moving relative to the
water?
• Same 2 questions, but downstream
Draw a model
• A certain fish can swim 4.6 m/s relative to water that isn’t moving. If there is a current moving at a speed of 1.3 m/s relative to the river bank, how long will it take the fish to swim 200m upstream?
SOHCAHTOA
• Sin Angle = Opposite over Hypotenuse
• Cosine Angle = Adjacent over Hypotenuse
• Tangent Angle = Opposite over Adjacent
• SOHCAHTOA gives us ratios of sides
In this class
• We will describe everything in 2 dimensions, North South (Up Down) and East West (Right Left)– Later on if you enjoy physics you can do 3-d
models
Describing Angles
• Determine which direction you are closest too (NSEW). This will be your 2nd direction stated– X degrees direction of direction
• Determine which direction you are moving away from the line– If North/South, then East/West off of line– X Degrees direction of direction
Describing Angles
• Determine how many degrees off the line by using some algebra– X degrees direction of direction
Vector Resolution
• A man travels 9 miles north and then travels 12 miles east.– Describe the man’s movement using
X degrees direction of direction
Vector Resolution
• A bird travels 8 miles south and then travels 6 miles east. – Describe the bird’s movement using
X degrees of direction of direction
Magnitude of displacement
• Displacement away from origin
• Pythagorean (or sohcahtoa)– A2 + B2 = C2
• Add to our description of movement– Blank units at X degrees direction of direction
Vector Resolution
• A bird travels 26 miles at 30 degrees E of North.– How many miles North did the bird travel?– How many miles East did the bird travel?
Vector Resolution
• A car travels 80 miles at 20 degrees S of E– How many miles South did the car travel?– How many miles East did the car travel?
Combining Vectors
• 10 miles North + 10 miles East = Not 20 miles
• 10 miles North + 10 miles North = 20 miles North
• Combine like terms on following or cancel as needed (North cancels South, East cancels West)
Vector Resolution
• A man travels 5 miles north, then travels 4 miles east, then 6 miles west.– Describe the man’s movement using
Blank miles X degrees direction of direction