Addition of Vectors Lab
Overview:
In this activity, you will use both the tail-to tip method and the trigonometric method of vector
addition in order to determine the resultant displacement of a trip that has two individual "legs."
Materials: ruler, protractor, pencil, calculator, two copies of a midwestern USA map
Head-to-Tail Method of Determining the Resultant:
!
!
A
B
On the attached map, use the indicated scale to add the
vectors
and
in a tail to tip
Include an
!
!
! fashion.
!
arrowhead !on each vector and label them clearly as A and B . Draw the resultant of A + B on the diagram and
label it as R . Begin at St. Louis, MO.
All angles are measured with regard to the “compass rose” shown in the lower right corner of the map.
Scale on map: _____ cm = 300 km
In the space provided, show the scaling calculation in the form of a unit conversion.
!
A
787 km at 38.0° N of E
scale length = _________ cm
!
B
908 km at 18.5° N of W
scale length = _________ cm
!
R
Scale length of resultant = _________ cm
Actual magnitude of resultant = _______________ km
Direction of Resultant _______________
Resultant Displacement for this trip is ___________________________________
The final destination appears to be in or at least close to the city of ________________________ in the state of
___________________.
Is this reasonable? Check your answer at http://www.convertunits.com/distance/
Now break the resultant vector from your tail to tip analysis into its x (east/west) and y (north/south)
components. Draw these components in red on your map.
scale length of x-component = _______________cm
scale length of y-component = _______________cm
How far north/south of St. Louis are you when you reach your destination? (show work below)
How far east/west of St. Louis are you when you reach your destination? (show work below)
Trigonometric Method of Determining the Resultant:
You will now use a calculator, trigonometric functions, and principles of vector resolution to solve the same
problem. You will sketch each displacement vector, determine, using trigonometry, the components of each
vector, and then record both the magnitude and direction for each component in the data table. Finally, you will
add all the components in the x-direction to determine the net x and all of the components in the y-directions to
determine the net y. Finally, you will sketch the vector diagram which shows how the net x-component adds
vectorally to the net y-component. Finally, you will
! use
! the Pythagorean theorem and trigonometry to determine
the magnitude and direction of the resultant of A + B
In the space below each vector described, show a diagram that breaks the given vector into its x- and ycomponents. Show components in red. Then use right triangle trigonometry to determine the magnitudes of the
components in the box to the right of your diagram. Show all work. Include your sign conventions.
!
A
787 km at 38.0° N of E
!
B
908 km at 18.5° N of W
Fill in the table below using the information from your calculations above.
vector Description of vector
x-component y-component
!
A
!
B
!
R
Use the magnitudes and directions from the table above to draw a vector diagram using the net-x and net-y
components. Then use the Pythagorean theorem and right triangle trigonometry to determine the magnitude and
direction of the resultant displacement.