Vector Addition Spreadsheet Lab
Names _____________
This lab adds vectors to calculate the resultant vector (magnitude and angle) and takes vectors apart into their
X and Y components. Your will be successful with this lab if you read and follow the directions carefully.
Create the Vector Spreadsheet
Create a new blank workbook in Microsoft Excel. Open Excel and go to file and select new on the upper tool
bar.
Insert the following text in your workbook. When creating a string of text just select the beginning cell and
keep typing the test. It will automatically expand the cell to fit the text.
SAVE your workbook. Since I have logged onto the computers, you can save it to ke_lpollack$ drive. Look for the Physics
folder and the correct period.
When you have completed this have your teacher initial here. ________________
The next step is to enter values and formulas for calculating the answers.
To take about a vector, for example: A Physics student runs 22 meters at an angle of 105 degrees from the positive xaxis.
In cell B6 enter the value 22. (This is the magnitude of the vector)
In cell B7 enter the value 105. (This is the angle from the positive X axis for the vector)
This is the test vector for Part I when we find the x and y components of a vector.
The formulas go into cell B11 and B12 to calculate the x and y components of the vector.
To solve for the x component, the basic formula is cos(105) =
x
.
22
Solving for x: x = 22 cos(105).
In order to enter this in the spreadsheet we must consider several things. The COS function only works on the angle if it
is in RADIANS. We must put a formula into the spreadsheet to convert the angle from degrees to radians.
Click on B11 and type in:
=B6*COS(RADIANS(B7))
Then hit the ENTER key. Be sure that there are two )) close parentheses at the end.
If you have done this correctly you should see the result below.
Here is what it means. It says take whatever value is in cell B6 (which is where the magnitude of the vector is entered)
and multiplies it by the cosine of the angle entered in cell B7. The formula fixed the angle so it was in radians.
The same thing must be done for the y component. The formula for B12 is y = 22 sin(105) which needs to be converted
to radians.
Click on B12 and type in:
=B6*SIN(RADIANS(B7))
Then hit the ENTER key.
The top portion of the spreadsheet should look like this:
If you have gotten this far correctly you have done a GREAT job. If things are not correct, ask your teacher or another
student to help you now before you go on.
Part I: Finding the x and y components of a vector
For the following vectors enter the magnitude of the vector is cell B6 and the angle from the positive X-axis in cell B7.
Draw a sketch of each vector and enter the x and y component of each vector.
1. 45 m/s at 30 degrees
x- component = __________________
y-component = __________________
2. 133 m/s at 124 degrees
x-component= __________________
y-component= __________________
3. 445 m/s at 245 degrees
x-component= __________________
y-component= __________________
4. 24 m/s at 330 degrees
x-component= __________________
y-component= __________________
Make sure the x and y components have the correct sign
for the quadrant where they are located
Part II: Adding Vectors in Component Form
Find Row 14 where is says Part II-Adding Vectors in component form. You will be using this portion of the spreadsheet.
Look at row 17 to 26. You will enter the x-component for up to 10 vectors in cells B17 – B26 and the y-components for
up to 10 vectors in cells C17 – C26.
Enter the values for the x-component and y-components for the 4 vectors shown below in row 17 through 20.
This portion of the spreadsheet will sum up the x and y components and then calculate the magnitude of the resultant
vector and the angle of that vector. The formulas to do this must be added as shown below.
In cell B28 enter the formula
=SUM(B17:B26)
In cell B29 enter the formula
=SUM(C17:C26)
These two formulas tell the spreadsheet to sum up all the numbers in the range of the cells specified.
To determine the magnitude of the resultant vector you will use the Pythagorean Theorem, C2 = A2 + B2
In cell B31 enter =(B28^2+B29^2)^0.5
This formula tells the spreadsheet to square the contents of cell B28 and then add to that to the square of the contents
of B29 and then raise that sum to the ½ power (which is the same as taking the square root of it).
In cell B32 enter =DEGREES(ATAN(ABS(B29)/ABS(B28)))
This tells the spreadsheet to give the number of degrees in the ArcTANgent (ATAN) which is the same as the TAN-1 of the
ratio of the opposite to the adjacent legs. The ABS function takes the ABSolute value of the legs.
In cell B33 enter
=180-B32
In cell B34 enter
=B32+180
In cell B35 enter
=360-B32
These will correctly calculate the number of degrees from the positive axis depending on what quadrant the resultant
vector is in.
Your spreadsheet should not look like this:
You will determine which angle to use from cells B32, B33, B34, or B35, depending on the signs of the X and Y
components of the resultant vector. Look at cell B28. What is the sign of the X component? _______. Now look at cell
B29. What is the sign of the Y component? ______. Choose the angle from the values in B32 to B35.
Since the x and y components are both negative the correct angle is 216.87 degrees.
Below is a sketch of the final answer. Notice that the angle is given as the angle from the positive x-axis. This determines
the quadrant of the answer. (This is the same as being 36.87 degrees below the –x axis in quadrant III).
216.87o
Part III – Problems
Use the top portion of the spreadsheet to take apart vectors into their x and y components.
Use the bottom portion of the spreadsheet to add up to 10 vectors to find the resultant vector and its angle.
1. A directionally impaired sailor walks 0.75 km east, 1.33 km north, 2.1 km west, and 0.45 km at an angle of 34
degrees north of east. Determine his displacement. (Hint #1 – Use the top portion of the spreadsheet to find
the x and y components of the 4th vector) (Hint #2 – the vector for 2.1 km west is x = -2.1, y = 0)
Displacement = _______________ km at an angle of ______________ degrees from East.
Explain the steps you used to solve this problem with the spreadsheet.
Attach a printout of your spreadsheet with your displacement and angle circled.
2. A jet airliner is flying at 550 mi/hr at a heading of 23 degrees north of west. (Be careful how you enter the angle
value!! You must input the degrees from the positive x axis.) The wind is blowing at 41.2 degrees south of east
with a speed of 133 mi/hr. What is the resultant velocity of the airliner?
Velocity = _________________ mi/hr at an angle of _______________ degrees from the East.
Explain the steps you used to solve this problem with the spreadsheet.
Attach a printout of your spreadsheet with your velocity and angle circled.
3. Make up your own original vector problem. Your journey should start in room 210. You can walk to the hall and
then up and down the 2nd floor halls. Please don’t go downstairs because that will add a third dimension to your
vector problem. You should have at LEAST 3 different vectors. Bonus points will be awarded for vectors that
include an angle and problems with creativity and originality.
a) Write out the complete description of the problem.
b) Explain how you used the spreadsheet to solve the problem.
c) Attach a printout of the solution with your displacement and angle circled.