2.11.2Project:Performance Task: The Parallax Problem

Project

Geometry Sem 1 (S3537251)

Julio Duenas

Points possible:120

Date: ____________

The Scenario:You're looking for a sponsor to pay for you to participate in a sailboat race. Now that you've solved the parallax problem, use the same skills you used there to proposal that shows that you can win the race.

The Project:Use the information provided in the performance task to estimate your travel costs and to calculate your average speed and the speed of last year's winner. Use the questions below to help you gather information to proposal.

Part I: Your City (8 points)

1. Which city did you pick and why? (2 points)

Sidney because I'd like to go there

2. What is one common boating hazard in this city? (2 points)

It is shallow , but busy.The hazrds include rocks stingrays and sharks

3. What are your total travel expenses? (4 points: 2 points for airfare/hotel. 1 point for total)

My round trip air fare is $2000.My hotel is $250/night for 10 nights or 2500.

My total travel expense is $4500

Part II: Your Boat (10 points)

1. Which boat did you choose and why? (2 points)

Catamarran since it is less likely to turn over.

2. What is one advantage of your boat? (2 points)

it is faster

3. What is one disadvantage of your boat? (2 points)

harder to turn back over if it capsizes

4. For the city and boat you picked above, what were the speeds of your last three races (in knots)? (2 points)

6.09 9.90 9.90

5. What is your average race speed? (2 points)

8.61

Part III: The Olympic Triangle (22 points)

1.Draw a sketch of the short course triangle below, labeling the pointsA,B, andC. Don't draw it on your master map yet! (3 points)

2. Draw the arrows to represent your path along the course. (3 points)

3. Where do you start? (3 points)

point a

4. What are the measures for anglesBandC? (3 points)

60 degrees

5. What is the measure for angleA? (3 points)

60 degrees

6. What do you know about the distance between each buoy? (3 points)

They are equal

4. What are the measures for angles B and C? (3 points)

60 degrees

5. What is the measure for angle A? (3 points)

60degrees

6. What do you know about the distance between each buoy? (3 points)

They are eqaul

7. The wind is blowing opposite to leg AB. Given the fact that you're traveling in a wind-powered boat, which leg of the course will take you the longest? Why? (4 points)

Part IV: Last year's winner (17 points)

1. What was the winning time of last year's race for your city and boat? (2 points, one for each leg)

2. Do you know how fast last year's winner was traveling? (2 points)

3. What information do you need to know in order to calculate last year's winning speed? (2 points)

4. What is thedefinitionof a knot when referring to boat speeds? (2 points)

5. How many feet are in a nautical mile? (2 point)

6. If you are traveling at 1 knot, how many feet per minute are you traveling? Remember that there are 60 minutes in an hour. Round to the nearest foot. (4 points: 3 points for setting up the problem, 1 for the answer)

7. You will use this number to calculate your speed. If you travel 1000 feet in 5 minutes, what is your speed in knots? (3 points: 1 point for finding the speed in feet/min, 1 point for converting to knots)

Part V: The Map (20 points)

Now you're going to use your knowledge of parallax to find the distance of the race course. Below is a grid to draw your Master map on. Use this to draw your parallax triangles and distances. Don't worry about drawing your map to scale. The grid is there to help you draw straighter lines.

1. What are the two landmarks from your city that you'll use for parallax? (2 points)

2. What is the distance between your two landmarks? (2 points)

3. Call the North LandmarkL1and the South LandmarkL2. Sketch the pointsL1 andL2 on your map. (2 points)

4. What is the fixed point in the water that you will use for parallax? (2 points)

5. Call your fixed pointP. Sketch the pointPonto the map. (2 points)

6. What is the distance from your fixed pointPto the line betweenL1 andL2 (calledL1L2)? (2 points)

7. Draw the line from your fixed point P to the lineL1L2 and add to the length of this line. (2 points)

8. Label the point of intersection between lineL1L2 and the new line as pointD. (2 points)

9. What is the distance fromL1 toD? That is, what is the measure of the line segmentL1D? Hint: review the diagram in "The Race Course" section of the Performance Task. (2 points)

10. What is the distance fromL2 toD? That is, what is the measure of the line segmentL2D?(2 points)

Part VI: Solving the problem.

Draw the Olympic triangle on your map. (10 points)

1. Buoy markerAwas set so that it's in a perfect line of sight with the hazard buoy and the landmarkL2. Draw buoyAso that it's in the proper line. You can choose the position of buoyA. (2 points)

2. The first leg of the racing triangleABruns parallel to the bridge. Draw this line. (2 points)

3. Buoy markerBwas set so that it's in a perfect line of sight with the hazard buoy and the landmarkL1. Draw buoyBso that it's on the parallax line. (2 points)

4. Sketch buoy markerC, remembering what you know about the Olympic triangle. Don't worry if your drawing is not to scale. (2 points)

5. What is the distance from the hazard buoy to racing buoyA? Hint: review the diagram in "The Race Course" section of the Performance Task.put distance on your map. (2 points)

Part VII: Calculate the distances. (23 points)

1. What is the distance from the hazard buoyPto the southern landmarkL2? Use this formula:, wheredis the distance fromPtoL2,DL2 is the distance fromDtoL2, andPDis the distance fromPtoD. Round to the nearest foot. (5 points)

2. What triangles are similar? How do you know? (5 points)

3. What is the distance between buoyAandB? (5 points)

4. What are the lengths of the other two triangle legs? (4 points: 2 points each)

Remember what you know about the shape of the Race Course.

5. What is the total length of the race course? (4 points: 3 for calculation, 1 for answer)

Part VIII: Calculate the winner's speed. (10 points)

1. What was the winner's speed during last year's race? (5 points. 3 points for speed. 2 points for conversion to knots).

2. How does the winner's speed compare with your average speed? How much faster or slower are you? (5 points)

C

Part IV: Last year's winner (17 points)

1. What was the winning time of last year's race for your city and boat? (2 points, one for each leg)

16.5 minutes

2. Do you know how fast last year's winner was traveling? (2 points)

no

3. What information do you need to know in order to calculate last year's winning speed? (2 points)

Distancetraveled

4. What is the definition of a knot when referring to boat speeds? (2 points)

Knot = 1 nautical mile/ hour

5. How many feet are in a nautical mile? (2 point)

6076 feet/ nautical lmile

6. If you are traveling at 1 knot, how many feet per minute are you traveling? Remember that there are 60 minutes in an hour. Round to the nearest foot. (4 points: 3 points for setting up the problem, 1 for the answer)

6076=x

601

X= 101.2 ft/min

7. You will use this number to calculate your speed. If you travel 1000 feet in 5 minutes, what is your speed in knots? (3 points: 1 point for finding the speed in feet/min, 1 point for converting to knots)

Part V: The Map (20 points)

Now you're going to use your knowledge of parallax to find the distance of the race course. Below is a grid to draw your Master map on. Use this to draw your parallax triangles and distances. Don't worry about drawing your map to scale. The grid is there to help you draw straighter lines.

1. What are the two landmarks from your city that you'll use for parallax? (2 points)

Hazard Buoy and north tower

2. What is the distance between your two landmarks? (2 points)

1700 feet

3. Call the North Landmark L1 and the South Landmark L2. Sketch the points L1 and L2 on your map. (2 points)

4. What is the fixed point in the water that you will use for parallax? (2 points)

Hazard buoy

5. Call your fixed point P. Sketch the point P onto the map. (2 points)

6. What is the distance from your fixed point P to the line between L1 and L2 (called L1L2)? (2 points)

7. Draw the line from your fixed point P to the line L1L2 and add to the length of this line. (2 points)

8. Label the point of intersection between line L1L2 and the new line as point D. (2 points)

9. What is the distance from L1 to D? That is, what is the measure of the line segment L1D? Hint: review the diagram in "The Race Course" section of the Performance Task. (2 points)

10. What is the distance from L2 to D? That is, what is the measure of the line segment L2D? (2 points)

Part VI: Solving the problem.

Draw the Olympic triangle on your map. (10 points)

1. Buoy marker A was set so that it's in a perfect line of sight with the hazard buoy and the landmark L2. Draw buoy A so that it's in the proper line. You can choose the position of buoy A. (2 points)

2. The first leg of the racing triangle AB runs parallel to the bridge. Draw this line. (2 points)

3. Buoy marker B was set so that it's in a perfect line of sight with the hazard buoy and the landmark L1. Draw buoy B so that it's on the parallax line. (2 points)

4. Sketch buoy marker C, remembering what you know about the Olympic triangle. Don't worry if your drawing is not to scale. (2 points)

5. What is the distance from the hazard buoy to racing buoy A? Hint: review the diagram in "The Race Course" section of the Performance Task. put distance on your map. (2 points)

Part VII: Calculate the distances. (23 points)

1. What is the distance from the hazard buoy P to the southern landmark L2? Use this formula: , where d is the distance from P to L2, DL2 is the distance from D to L2, and PD is the distance from P to D. Round to the nearest foot. (5 points)

2. What triangles are similar? How do you know? (5 points)

3. What is the distance between buoy A and B? (5 points)

4. What are the lengths of the other two triangle legs? (4 points: 2 points each)

Remember what you know about the shape of the Race Course.

5. What is the total length of the race course? (4 points: 3 for calculation, 1 for answer)

Part VIII: Calculate the winner's speed. (10 points)

1. What was the winner's speed during last year's race? (5 points. 3 points for speed. 2 points for conversion to knots).

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