Vector Addition

many directions where to go by flickr user regolare

State the magnitude and direction of each vector.

HOMEWORK

State the magnitude and direction of each vector. (You can determine the answer using ruler and protractor.)

HOMEWORK

Draw scale diagrams of the following vectors using pencil, ruler, protractor, and paper. Label the diagram. Be sure to indicate the scale you used.

(b) A boat is headed 300° at 45 km/h.

(a) Tiffany walks 13 blocks in a direction E15°S.HOMEWORK

A ball is thrown horizontally against a wall with a velocity of 10 m/s. It rebounds with a velocity that has a magnitude of 75% of the initial velocity. Sketch two vectors to represent the two velocities.

HOMEWORK

Adding Vectors Using Scale Diagrams ...

When two vectors are added a new vector is made. It is called the RESULTANT vector.

Vectors can be added an any order.

When a vector is moved around in a plane it is considered to be the same vector. These two vectors are considered to be identical:

A vector is represented by an arrow. It's LENGTH determines it MAGNITUDE and the TIP determines its DIRECTION.

There are two techniques that we use to add vectors using a scale diagram ...

TIP

TAIL

A ball is thrown horizontally against a wall with a velocity of 10 m/s. It rebounds with a velocity that has a magnitude of 75% of the initial velocity. Sketch two vectors to represent the two velocities.Visualizing the Process ...

Vector Calculatorhttp://comp.uark.edu/%7Ejgeabana/java/VectorCalc.html

Resultant of Forces(Addition of Vectors)http://www.walter-fendt.de/ph14e/resultant.htm

The Triangle Method

The Parallelogram Methodtail-to-tail

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The Parallelogram Method ...We use the parallelogram method when the vectors are arranged tail-to-tail.

We find the "answer" by measuring the length of the resultant vector and it's bearing using a ruler and protractor.The length of the result vector often has to be converted to appropriate units using the given scale.

Scale: 1 cm = 2 km

The Triangle Method ...

We use the triangle method when the vectors are arranged tip-to-tail.

Scale: 1 cm = 2 km

Remember, we use measurements with a ruler and protractor to find the "answers."

RESULTANTRESULTANT

You try ...

Add each pair of vectors using the parallelogram method.

is 3 meters eastis 4 meters north

is 3 meters southwestis 4 meters west

Find FindHOMEWORK

You try ...

Add each pair of vectors using the triangle method.

is 3 meters eastis 4 meters north is 3 meters southwest

is 4 meters west

Find Find

HOMEWORK

Now let's apply what we've learned in some problems ...

Bruce and Jeff paddle their canoe 5.5 kilometres west, and then paddle four kilometres south. How far are they from their starting point? What direction must they paddle to return to the starting point by the shortest route?

HOMEWORK

Forces of 210 N and 85 N act at an angle of 78° to each other. Find the resultant force and the angle it makes with the smaller force.

HOMEWORK