Vector Addition

Chapter 4

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

• Done by placing vector lines end to end (in appropriate direction)

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?

Vectors Addition Algebraically

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

• 30 degrees N of E or 60 degrees E of N (for left)

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

Vector Resolution

• A bird travels 7 miles South, then travels 2 miles East, and then 4 miles North – Describe the bird’s movement using

Blank miles X degrees direction of direction