Virtual Activity: Working with Vectors
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!