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Physics 11 Kinematics – Vector Analysis Treasure Hunt

Objectives: Students will be expected to…

Use vectors to represent position, displacement, velocity, and acceleration (325-5)

Activity Description:

The class will be divided into groups of 2-4, depending on class size. Ideally smaller groups are better, and no more than 12 groups should be used in order to avoid chaos. Each group will be provided with a “map” of the school grounds (see Appendix A), with a scale and North compass included, the necessary materials listed below, an instruction sheet (see Appendix B) and their first clue. If unable to be performed outdoors due to weather constraints or school policies, the activity/map could either be altered to be used inside the school, or so that it could be done without physically travelling between points (ie at the students’ desks; see Appendix E). If possible, number the groups (1 to n) and try to have each group start at a different location so that everyone needs to actually solve their clues in order to complete the activity. When the group reaches their “treasure” there would be a small prize for each student (ooh, a pink protractor, awesome!).

Prior to class starting the teacher would have to place all of the “clues” in their correct location. Each clue would consist of a sheet of paper (see Appendix C) containing different vector components for each group, which they would have to solve in order to move on to the next clue. This is why it would be better to have each group numbered and following separate paths, so that no two paths are the same and students cannot just follow each other.

Possible Activity Extension for Assessment:

Students could be provided with an activity sheet (see example, Appendix D) that included further information for each clue (ie the time it took a bird to fly between the two points) and students would have to solve for the velocity, or acceleration, or be required to provide a graph, etc. This worksheet could be handed in and used as a form of assessment for learning, to see where any difficulties may lie. Note that there would have to be a different worksheet for each group that corresponded to their treasure map path.

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Another possible extension would be for students to create their own treasure maps (such as in Appendix A) and exchange them with other students in their class to solve.

Materials Needed:

Surveyor’s Wheels (to measure distance) Magnetic Compasses Protractor (360˚if available) 30 centimetre Ruler (with millimetres) Calculator Graph Paper

Appendix A – Sample Map

Street

Woods

Fence

A

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Appendix B – Sample Student Instructions

Treasure Map Directions – Group 1

Starting position “A” on map. Using the vector components marked “Group 1”, as well as your map

and other materials, to find the resultant displacement vector – draw this on your map (remember to use factor labelling to convert metres to centimetres!)

Using your compass and Surveyor Wheel, follow your displacement vector to your next clue.

Remember to write down the vector components at each clue – you will need these later to complete your worksheet.

Continue until you reach the clue that says “Group 1 – Finish Line” – here you will find your prize(s) in the baggy underneath the clue.

When you have successfully found your treasure, complete the worksheet – to be handed in next class.

I will be roaming around from group to group if anyone needs help. If you’re stuck on something, send one partner to get me while the other remains at your last clue.

NOTE: All the groups are following different paths, so if you try to follow another group you will end up in the wrong place.

Appendix C – Sample “Clue” Sheet

Clue D

Group 1 –24 metres East; 53 metres South-West; Clue B

Group 2 – 70.5 metres North; 2 metres North-East; Clue H

Group 3 – 17 metres West-South-West; 210 metres North-East; Clue E

Group 4 – 89 metres North-North-West; 118.5 metres South; Clue A

Group 5 – 29 metres South-East; 153 metres South-West; Clue G

Group 6 – 200 metres East; 192 metres South-South-East; Clue C

Group 7 – 127 metres South; 65 metres West; Clue F

0m 50m 100m

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Group 8 – 94 metres East-North-East; 23 metres North-West; Clue I

Appendix D – Activity Extension Sample Worksheet

Group 1 Worksheet

1. Find Max’s resultant velocity vector for each segment (as well as its

components), given the following times, and using the displacement

components from the treasure hunt clues (remember that velocity is

also a vector, which means it has a magnitude AND a direction). Draw

the resultant velocity vectors onto your blank map:

a. A to C – component 1: 35 seconds , component 2: 18 seconds

b. C to H – component 1: 12 seconds, component 2: 3 seconds

c. H to F – component 1: 48 seconds, component 2: 25 seconds

d. F to I – component 1: 9 seconds, component 2: 72 seconds

e. I to D – component 1: 24 seconds, component 2: 39 seconds

f. D to B – component 1: 62 seconds, component 2: 44 seconds

g. B to E – component 1: 43 seconds, component 2: 19 seconds

2. Max had lots of energy, so this time he decided to run between points.

Graph the following as a velocity vs. time graph (assume there is no

change in velocity when he switches direction, ie if he reaches point C

at 1 m/s, he also leaves point C at 1 m/s unless otherwise specified):

a. Max started off slow. He started at point A standing still, and

reached point C with a velocity of 0.84 m/s in 13 seconds.

b. It only took him 9 seconds to reach point H, and when he got

there he was running at 1.18 m/s.

c. Max is not in the best shape, so he started running out of breath

between points H and F. When he got to point F he was running

0.76 m/s, and it took him 21 seconds to get there.

d. Max decided to stop when he got to point I. It took him 17

seconds to get there, and once he stopped he stood to catch his

breath for 10 seconds.

e. Ready to go again, Max took off for point D, making it there in 14

seconds at a speed of 0.93 m/s.

f. There is a large hill between points D and B. It took Max 47

seconds to get there, and his speed at point B was only 0.24 m/s.

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g. For his sprint to the finish line Max got to run back downhill to

point E. It took him 11 seconds, and he passed the finish line

going 1.07 m/s.

h. He pulled up after he crossed the finish line. He ran/jogged an

additional 17 metres (in the same direction), coming to a stop in

6 seconds.

3. Calculate the slope of each segment of your graph. What do these

slopes represent?

4. Graph your calculated slopes on the Y-axis, with time on the X-axis.

Provide an appropriate title and axis labels.

BONUS:

What is the term for a change in acceleration over a change in time?

Can you provide an example of when you may have experienced this?

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Appendix E – Activity Adaptation (for inside the classroom)

Students would have to use provided information and draw vectors on their map. Once they completed all of the clues and drew all the vectors correctly, the resulting position would be a specific point on the map (ie the Chemistry Lab); when students thought they had the correct answer they would verify it (quietly) with the teacher, who would then either provide them with a prize, or point out where they may have made slight errors. Once this portion was finished, students could complete an extension worksheet (see Appendix D) to be handed in.