1.7 Graphical Methods of Vector Addition

​1.7 Graphical Methods of Vector Addition

• ​Scalars are quantities (mass, length, or speed) completely specified by magnitude & have no direction.

• Vectors are quantities possessing both magnitude and direction and can be represented by an arrow; the direction of the arrow indicates the direction of the quantity and the length of the arrow is proportional to the magnitude.

• Vectors that are in 1 dimension can be added arithmetically.

• Vectors that are in 2 dimensions are added geometrically.

• When vectors are added graphically, graphs must be done to scale and answers are only as accurate as the graphing.

​In physics, a quantity, such as mass, length, or speed that is completely specified by its magnitude and has no direction is called a scalar. 
A vector, on the other hand, is a quantity possessing both magnitude and direction. A vector quantity is typically represented by an arrow-tipped line segment. The length of the line, drawn to scale, represents the magnitude of the quantity. The direction of the arrow indicates the direction of the vector.

Not only can vectors be represented graphically, but they can also be added graphically.

Multiple Choice

What is a magnitude?

• A numeric value.
• A direction.

Multiple Choice

A scalar is a magnitude _____.

• With direction.
• Without direction.

Multiple Choice

Distance

• Vector
• Scalar

Multiple Choice

Distance and direction of an object's change in position from a starting point

• displacement
• distance
• motion
• reference point

Multiple Choice

Which is NOT a correct Vector?

• 45N up

• 6N -->

• 20N

• 22N North

Dropdown

The measurement 32 degrees Fahrenheit is a ​ ​

Select answer

Multiple Choice

Is this a scalar quantity or a vector quantity?
A deer running 15 meters per second due west

• Scalar
• Vector

​For 1 dimensional vector addition, the 1st vector is placed on a number line with the tail of the vector on the origin.  The 2nd vector is placed with its tail exactly on the arrow head of the first vector.  The sum of the two vectors is the vector that begins at the origin and ends at the arrow head of the final added vector.

Multiple Choice

How do you combine vectors if they are in opposite directions?

• Add
• Subtract
• Pythagorean Theorem
• Use trigonometry

Multiple Choice

What is the resultant of these two vectors?

• +17 m

• +3 m

• -17 m

• -3 m

Multiple Choice

What is the resultant vector of the two labeled vectors?

• +2 km

• +14 km

• -2 km

• -14 km

​The graphical process for adding vectors in two dimensions is to place the tail of the second vector on the arrow head of the first vector as shown above.

The sum of the two vectors is the vector that begins at the origin of the first vector and goes to the ending of the second vector, as shown.

Multiple Choice

Another name for the "tip" of the vector

• Terminal point

• Initial point

• Standard position

• Direction

Multiple Choice

Another name for the "tail" of a vector

• Terminal Point

• Standard Position

• Initial Point

• Magnitude

​If we are using totally graphic means of adding these vectors, the magnitude of the sum would be determined by measuring the length of the sum vector and comparing it to the original standard.

We would also use a compass to measure the angle of the summation (resultant) vector.

The length of the sum vector can also be determined mathematically by the Pythagorean theorem,  a²+b²=c². 

The length of the hypotenuse would be the square root of (121 + 121) or 15.6 Km.

Multiple Choice

If vectors X and Y are added, then the resultant would be best represented by vector _____. 

• A
• B
• C
• D

Multiple Choice

Vector A is directed northward and vector B is directed eastward. Which of the following vector addition diagrams best represent the addition of vectors A and B and the subsequent resultant?

• A

• B

• C

• D

• E

Multiple Choice

In practice A of the figure, What is  the magnitude of the  resultant displacement?

• 5 km 
• 8 km
• 11 km
• 15 km

Multiple Choice

In practice A of the figure, what is the direction of the resultant displacement?

• 63 degrees, South of East
• 63 degrees, North of West
• 27 degrees, North of West
• 27 degrees, South of West

Multiple Choice

Solve for the missing angle. Round the nearest degree. 

• 50
• 1
• 37
• 95

Multiple Choice

When adding vectors graphically, the magnitude of the resultant vector is represented

• the length of the vector drawn

• the arrow head of the vector drawn

• both of the above

• none of the above

Multiple Choice

What is the Net Force?

• 5 N to the right
• 10 N to the right
• 15 N to the right
• 0 N

Multiple Choice

The president’s airplane, Air Force One, flies at 250 m/s to the east with respect to the air. The air is moving at 35 m/s to the north with respect to the ground. Find the velocity of Air Force One with respect to the ground.

• 252 m/s
• 222 m/s
• 435 m/s
• 125 m/s