## Vectors Lab

*Modified from "Vectors Activity" created by Amy Jordan – Evergreen High School, Colorado*

Use the simulation below to answer the following questions.

Procedure:

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

Procedure:

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.**1. You go for a walk and take 20 steps in the north direction (90°). Use the simulation to represent your path.**

**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?

a)

**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.

**3. You are flying a hang glider at 14 mph in the northeast direction (45°). The wind is blowing at 4 mph FROM due north.**

**a)**What is your airspeed?

**b)**What angle (direction) are you flying?

**c)**The wind increases to 14 mph from the north. Now what is your airspeed and what direction are you flying?

**d)**If your destination is to the northeast, how would you change your speed or direction so you might make it there? Test your answer using the simulation.

**4. You hike for 1.9 hours at a speed of 3 mph in the southwest direction (-135°). Then you head ESE (-16º) for 7.3 miles at the same speed.**

a)How many miles have you

a)

*hiked*?

**b)**How many miles is your destination from your starting point (as the crow flies).

**c)**What direction is your destination from your starting point? What would a compass read?

**d)**For how many hours have you hiked?