VectorsCh. 3.1-3.3

Objectives

1. Vector vs. Scalar quantities

2. Draw vector diagrams

3. Find resultant of two vectors

The Wind

• Do we run faster with the wind or against the wind?

• Have you ever been on a plane flight that’s early or late due to wind?

• When talking about wind, we are talking about magnitude and direction

Strength of the wind

• If we draw arrows comparing a strong easterly wind vs. a weak westerly wind, how would we do that? Give it a try.

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Magnitude

• Magnitude – any number

• Scalar Quantity:– Quantity that is described by a magnitude, or number,

only.

• Examples of scalars: 1 km/h, 8 kg of sand, 22 years old. These are all “scalars.”

• Can be added, subtracted, divided, and multiplied.

Vector

• What’s a vector?

• Vector:– Number (magnitude) and direction

• How can we illustrate vectors?– You already did this by drawing those arrows!– Vector Example: Bay Area Wind Patterns

Vector Diagrams

• All vectors have a tail and a head.• Draw the vector above and label it.

Vector Addition• Two vectors can be

added up to form the result, or resultant

• Copy a couple of the examples in this diagram

Vector Addition• How fast would an bird

move if it had an airspeed of 7 km/h when flying into a headwind of 7 km/h? Draw a diagram, and check w/ your neighbor

• Speed of 0 km/h!– Like birds are often

seen when facing a strong wind

Vector Addition

• Plane flying at 80 km/h with a crosswind of 60 km/h

• We use the Pythagorean Theorem• c2 = a2 + b2

• Resultant2 = (80km/h)2 + (60 km/h)2

• Resultant2 = 6400km/h + 3600km/h = 10,000km/h

• Square root of 10,000km/h = 100km/h

• Let's see

Do planes go faster when flying in cross winds?

Practice Problem

• How fast will a boat that normally travels 10 km/h in still water be moving with respect to land if it sails directly across a stream that flows at 10 km/h?

• Draw the diagram• c2 = a2 + b2

• Resultant2 = 102 + 102

• Resultant2 = 200• Square root of 200 = 14.14 km/h

Practice Problem• A plane is flying at 200 km/hr with no wind.

If a crosswind of 50 km/hr develops, will it affect the speed of the plane? If yes, by how much?– c2 = a2 + b2

– C2 = 2002 + 502

– C2 = 40,000 + 2,500– Square root of 42,500– 206.16 km/hr

Vectors and Surfing

Vectors and Surfing1. Surfing in the same direction of wave --> surfer’s velocity =

wave’s velocity2. Shows two velocity components which result in a third velocity:

the velocity of the surfer traveling perpendicular to wave as well as parallel to wave. This makes the surfer go faster.

3. The velocity of the wave stays the same. Can the surfer change his/her velocity?

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• How can we vary the velocity of surfer?

• Increase/decrease the angle!

• Resultant velocity, is found by the Pythagorean Theorem.

• Surfer’s adjust their vectors depending on what the the wave does

• Let’s watch a few quick clips . . .

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Vectors can be applied to baseball as well!