**Virtual Activity: Working with Vectors**

The lab report for this activity should include:

1. The title of the lab activity

2. The date the lab activity was performed

3. The goal(s) of the lab activity

4. A description of the lab activity. In this case you should include a procedure (a list of steps that you followed) along with a screen shot of the simulation without any vectors in the grid.

5. Data collected in the lab activity For this lab report, show screen shots of the simulation, including the vectors in the grid, for each of the problems you work on.

6. Analysis of data (the calculations in this case)

7. Conclusion(s) (What did you learn in this lab exercise? Be specific.)

There is no error analysis in this lab.

In this activity you will practice adding vectors together using the simulation shown on the bottom of this page. Read through these instructions and then work on the three problems below.

**Instructions**

Choose the "Explore 2D" simulation.

Drag vector

**a**onto the grid.

Change the size and orientation of the vector by moving its tip to various locations.

Drag vector

**b**onto the grid.

Change the size and orientation of the vector by moving its tip to various locations.

Click the "Sum" box to see the addition of the vectors.

Now click the "angle" box to show the angle of each vector. Note that the angle is measured from the + x axis and that an angle of -90° is equivalent to an angle of 270° and so forth.

Finally, move the vectors around to show that vector

**a**plus vector

**b**form a head to tail addition to produce the sum (vector

**s**).

Problem 1: In your lab notebook, calculate the sum of the following two vectors:

Vector **A**: magnitude = 16.2, angle = 21.8°

Vector **B**: magnitude = 10.0, angle = 5.7°

Now use the simulation to connect these vectors head to tail. Click the show sum box and compare your answer to that given in the simulation. You should slide the resultant vector into the space from the tail of vector **A** to the head of vector **B**.

Problem 2: In your lab notebook, calculate the sum of the following three vectors:

Vector **A**: magnitude = 9.4, angle = 32.0°

Vector **B**: magnitude = 13.9, angle = 59.7°

Vector **C**: magnitude = 15.0, angle = -143.1°

Now use the simulation to connect these vectors head to tail. Click the show sum box and compare your answer to that given in the simulation. You should slide the resultant vector into the space from the tail of vector **A** to the head of vector **C**.

Problem 3: In your lab notebook, calculate the sum of the following three vectors:

Vector **A**: magnitude = 17.1, angle = 159.4°

Vector **B**: magnitude = 6.4, angle = -51.3°

Vector **C**: magnitude = 12.0, angle = 4.8°

Now use the simulation to connect these vectors head to tail. Click the show sum box and compare your answer to that given in the simulation. You should slide the resultant vector into the space from the tail of vector **A** to the head of vector **C**.

Play around a bit! Have fun!