Question

Procedures: Go to http://phet.colorado.edu/ click on “Simulations,” and look for “Math Tools.” Click on the “Vector Addition” sim.

To get a vector, grab an arrow from the bucket. The length of the vector is found in the |R| box. The angle of the vector is in the θ box. Place the vectors you wish to add head to tail. To get the resultant vector, hit the big “SUM” button. Move the green sum vector so that the tail touches the tail of your first vector.

Answer 1

Data: Answer the following questions using the simulation. For each question, draw (and label with size and direction) the vectors you used in the sim. Use a protractor and ruler to draw the vectors accurately, and label the sum vector.

1. You go for a walk and take 20 steps in the north direction (90°). Use the simulation to represent your path. Draw and label your vector on your lab write-up.
a) Explain why this vector could also represent traveling at 20 mph in the north direction.
b) Next, you turn left and walk 10 steps to the west. Add the two vectors using the “sum” button. How far from where you started did you end up?
c) In math, 2+3=3+2. What is this property called? Does this property hold for vector addition? Try it with the scenario above by first walking 10 steps west and then walking 20 steps north. Compare the result to the sum in part b).

2. You are going for a drive, but a detour takes you out of the way of your destination. You drive north for 10 miles, turn right and drive east for 5 miles, turn to the north and drive for 3 miles, drive west for 10 miles, and arrive at your destination.
a) How far from where you started did you end up?
b) If you wanted to travel directly to your destination without following the streets (as the crow flies), what angle would you take? What direction would a compass read?
c) Now try adding the vectors in a different order. For example, start with the 5 miles east, then 3 miles north, etc., as long as you add all four vectors. Compare the result to the sum in part a). Draw the vectors in the order you used.

Answer 2

The tool link doesnt work, but i may be able to still help

Answer 3

20 mph north could be represented by a vector also, velocity is a vector value, it has both a magnitude (20) and the direction of the arrow, North

Answer 4

Vector S magnitude is found by the pythagorean theorem

\[\left| S \right| = \sqrt{10^2 + 20^2} = 10\sqrt{5} \approx~~22.36~~ steps\]

Answer 5

2 + 3 = 3 + 2 is the communitive property of addition. It also works for vector addition.
Notice if you walk sideways first then up, you will end up at the same spot and have formed a rectangle.
Parallelogram law of vector addition. Look that up.

Answer 6

21 degrees west of north, or (90-21) = 69 degrees north of West

Answer 7

You can draw the vectors in any order, the resultant vector will be the same... try it out

A+B+C+D = D+A+C+B (any order for vector addition) commutative property

Answer 8

Thank you for your help, also i fixed the link if you would like to try it now.