Warm Up

• 1) Draw a vector

• 2) Vectors are defined by their ____________and ___________.

Finish Test

Vectors• You CAN

– Move them– Describe them by their magnitude and direction

• Magnitude means length or strength

– Break them into x and y components, and use those to describe them

• Use Trig to find components

– Think of them as the hypotenuse of a right triangle.

• One leg, parallel to x axis is x component• One leg, parallel to y axis is y component

– Add (and Subtract) them

Vectors

• You CANNOT– Turn them (change their direction)– Make them longer or shorter

A Vector

Tail

TipMagnitude

Direction

Labeling Vectors

• Write the name of the vector with an arrow over it.– We can also write the name of the vector in

bold font

Adding Vectors

• When we add vectors we add them “Tail to tip”

• For instance if A + B = C then we take vectors A and B and we move one so that its tail is touching the tip of the other. To get the answer (Vector C) we draw a new vector from the tail of the first vector to the tip of the second vector

A B

A + BSee? Tail to Tip

A + B = C C

This is the answer

Moodle

• Respond to the prompt in the forum for this week.

• Read the prompt for next week. This is homework. Due Nov. 14

Components

This vector is 3 units long.

X component = 0

Y component = 3

This vector is 4 units long.

X component = 4

Y component = 0

Components

36.87°

5

The x component is the side along the x axis. This is adjacent to the angle. We will use cos to find its length

Vector C

This is Cx, the x component of C.

Magnitude of Cx = Length of C, Times the cosine of the angle or

Cx = C * cos 36.87Cx =5 * cos 36.87

Cx = 4

Components

36.87°

5

The y component is the side along the y axis. This is adjacent to the angle. We will use sin to find its length

Vector C

This is Cy, the y component of C.

Magnitude of Cy = Length of C, Times the sine of the angle or

Cy = C * sin 36.87Cy =5 * sin 36.87

Cx = 3

Cy

Components

• So vector C has– X component = 4– Y component = 3– Overall (or net) magnitude of 5

• Notice that the components and magnitude obey the Pythagorean theorem

Warm Up

Vector F has a magnitude of 10 and a direction of 53.2 degrees above the x axis.

• A) Draw F.

• B) Find the x component of F.

• C) Find the y component of F

Notebook

• Page 1 - 3 -Table of contents

• Page 4 - 7 - warm ups

• Page 7 - 14 - Notes

• Page 14 - 17 -Personal Physics Demons

• Page 18 - 30 - Practice Problems

• Page 31 - 50 - Homework

Adding vectors using components

• If we are adding two vectors, find the x and y components of each one.

• Add the x components up (direction matters!)– What you get is the x component of the

resultant

• Add the y components up– What you get is the y component of the

resultant

Adding vectors using components

• Use the components you found to make the resultant Vector

Homework

• Pg 65 (Q 5-8; P 4, 5, 7-9a)

• P10