Trigonometry & Vectors Guided NotesName:______

Why do we need trigonometry?

Trig allows us to calculate the ______or ______

We will use trig constantly in the first three quarters of physics … anytime something ______.

Examples:

Finding resultant velocity of a plane that travels first in one direction, then another

Calculating the time, path, or velocity of a ball thrown at an angle

Predicting the course of a ball after a collision

Calculating the strength of attraction between charges in space

etc., etc., etc

Right Triangles

The formulas that we learn today work only with right triangles … but that’s ok, we can create a right triangle to solve any physics problem involving angles!

But, it does beg the question … what’s a right triangle? ______

Calculating the length of the sides of a right triangle

If you know the length of two of the sides, then use ______

Example: A = 3 cm, B = 4 cm, what is C?

  • What if we have one side and one angle? How do we find the other sides?

______

Calculating the angles of a right triangle

  • In any triangle (right or not) the angles ______.

Example: Find a

  • In right triangles, we can also find the angle using the ______and ______

Introduction to Vectors Guided NotesName:______

What is the difference between scalars and vectors?

Scalar Example / Magnitude
Speed / 20 m/s
Distance / 10 m
Age / 15 years
Heat / 1000 calories

A ______is ANY quantity in physics that has ______, but ______.

A ______is ANY quantity in physics that has ______and ______.

How are velocity and speed related?

______

Example - 20 m/s = ______20 m/s NE = ______

What is displacement?

______

How to draw vectors

The ______of the vector, drawn to scale, indicates the ______of the vector quantity.

Example: Lady bug displacement

Quick Review

What is the difference between a scalar and a vector? What are the parts of a vector?

Adding Vectors: Plane example 1 – Tailwind

A small plane is heading south at speed of 200 km/h. (This is what the plane is doing relative to the air around it)

The plane encounters a tailwind of 80 km/h.

Adding Vectors: Plane example 2 – Headwind

A small plane is heading south at speed of 200 km/h. (This is what the plane is doing relative to the air around it)

It’s Texas: the wind changes direction suddenly 1800. Now the plane encounters a 80 km/h headwind

Adding Vectors: Plane example 3 – Crosswind

A small plane is heading south at speed of 200 km/h. (This is what the plane is doing relative to the air around it)

The plane encounters a 80 km/h crosswind going East.

Work the problem here!

The order in which two or more vectors are added ______.

Vectors can be moved around as long as their length (magnitude) and direction are not changed.

Vectors that have the ______and the ______are ______.

WE DO PROBLEMS

Example: A man walks 54.5 meters east, then 30 meters west. Calculate his displacement relative to where he started.

Example: A man walks 54.5 meters east, then again 30 meters east. Calculate his displacement relative to where he started.

Example: A man walks 54.5 meters east, then 30 meters north. Calculate his displacement relative to where he started.

You Do Problems

A person walks 5m N then walks 8m S. Calculate his displacement.

A ball is thrown 25 m/s E. A tailwind of 5 m/s E is blowing. Calculate the resulting velocity.

A boat moves with a velocity of 15 m/s, N in a river which flows with a velocity of 8.0 m/s, west. Calculate the boat's resultant velocity with respect to due north

A bear, searching for food wanders 35 meters east then 20 meters north. Frustrated, he wanders another 12 meters west then 6 meters south. Calculate the bear's displacement.

Multiplying a Vector by a Scalar

Multiplying a vector by a scalar will ______.

The exception: multiplying a vector by a negative number will ______its direction.

Vector Components and Adding Non-Perpendicular Vectors Name:______

Vector Components

Any vector can be “resolved” into two component vectors.

Ax is the horizontal component – or x component -- of the vector.

Ay is the vertical component – or the y component – of the vector.

Example A plane heads east, while the wind moves a plane north. As a result, the plane moves with velocity of 34 m/s @ 48°relative to the ground.

Calculate the plane's heading and wind velocity.

What does this mean??

It means we need to find the ______

______

Draw the diagram and solve the problem, below.

Example A plane moves with a velocity of 63.5 m/s at 32 degrees South of East. Calculate the plane's horizontal and vertical velocity components.

You Do problems

A person walks 450 m @ 120 degrees. Find the x and y component vectors.

A car accelerates 6 m/s2 at 40 degrees. Find the x and y component vectors.

You can reverse the problem and find a vector from its components.

Let:

Fx = 4 N

Fy = 3 N .

Find magnitude and direction of the vector

Diagram and solve the problem below.

Adding vectors at any angle

Example: Two people are lugging a heavy suitcase. One pulls with a 68N force at 24o; the other pulls with a 32 N force at 65O. What is the total force exerted by the two people on the suitcase?

Solving procedure

1)

2)

3)

4)

5)

6)

7)

Diagram and solve the problem below

You do

1)V1 = 35 m/s @ 28 degrees, V2 = 40 m/s @ 60 degrees Find V = V1 + V2

2)X1 = 4.8 km @ 140 degrees, X2 = 5.3 km @ 30 degrees Find X = X1 + X2

Hint: if the x or y components go in different directions, subtract the smaller from the bigger. You diagram will show you!