Applying Vectors

PhysicsK. Allison

Engagement

• If a plane and the wind are blowing in the opposite direction, then the plane’s velocity will decrease.

• Today we will learn how we can represent events like this.

Objectives

• Draw vectors and apply them to moving objects

• Evaluate properties of component vectors• Calculate the resultant given component

vectors• HONORS- calculate the horizontal and vertical

components from the resultant

Vectors

QuestionsWhat is a vector

quantity?

What is a vector?

FactsMagnitude and directionex. Velocity, Acceleration

An arrow- Represents something with

magnitude and direction- Line tells magnitude- Arrow tells direction

Drawing Vectors

• Draw a vector that represents a plane flying east at 110 km/h and another vector representing the wind blowing east at 35 km/h.

More about Vectors

TopicComponent vectors

FactsTwo or more vectors that

can be used to find a resultant.

More about Vectors

TopicResultant

FactsThe combination of two

or more component vectors

More About Vectors

QuestionsWhat is the

resolution?

FactsThe process of

determining the components of a vector

Steps to Finding Resultant1. Draw the vectors with their tails touching

2. Draw parallel projections of each vector to form a box (if applicable)

3. Draw the diagonal from the point where two vectors touch (if applicable)

Finding the ResultantA plane flies east at 90 km/h while the wind is

blowing east at 30 km/h. How fast is the plane actually flying?

This is an example of a plane experiencing a tailwind!

Finding the Resultant• Suppose and airplane flies 100 km/h east and

a wind blows 20 km/h west. How fast will the airplane travel?

• This is an example of a plan experiencing a headwind!

Headwind and Tailwind

QuestionsWhat is a headwind?

FactsThe wind is blowing in

the opposite direction of another object

• Coming head-on• Slows motion• Subtract

Headwind and Tailwind

QuestionsWhat is a tailwind?

FactsThe wind is blowing in

the same direction of another object

• Coming from behind (tail)

• Increases motion• Add

Reach for the Stars!

QuestionsSuppose that an airplane

normally flying at 80 km/h north encounters wind at a right angle to its forward motion- a westward crosswind. Will the airplane fly faster or slower than 80 km/h?

FactsThe airplane will fly faster

WHY??Pythagorean Theorem

a2 +b2 = c2

c2 is the resultant (in math the hypotenuse) which is longest

side of a triangleLongest side equates with

largest magnitude!

Finding the ResultantSuppose that an airplane normally flying at 80

km/h north encounters wind at a right angle to its forward motion- a westward crosswind. Will the airplane fly faster or slower than 80 km/h? How FAST?

HONORS- Reach for the Stars!

QuestionsIf given the

resultant, how can one calculate the horizontal and vertical components?

FactsTrig functions• Sine• Cosine• tangent

Trig Review

(H)-Finding the Component Vectors• A boat was trying to cross a river North but

the river was flowing west resulting in the boat moving 6 m/s northwest at a 45° angle to the horizontal. What are the horizontal and vertical components?

Find the Resultant/Components Recap

Topic1. Headwind

2. Tailwind

3. Components at Right Angles

Facts

HONORS- Find the Resultant/Components Recap

Topic1. Given resultant

and find components

Facts

Class work

Practice with TeacherComplete #19, 20,

23

HonorsComplete #19-24

Practice on Your Own Complete problems at

lab stations in back to turn in.

ClosingPut your name on the left side of blank paperWrite two problems that require vector

calculations:1. Headwind/tailwind2. Components at right angles to each other

Let your partner solve the two problemsThe partner should put his/her name on the right side of paper