applied math 40s april 18, 2008
DESCRIPTION
Geometric vector addition.TRANSCRIPT
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
>
>
>>tip
-to-ta
il
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