Module 3 Project

1. Module 3 Project

Mathematics 20-3 Module 3

Module 3: Slope and Rate of Change

 

Module 3 Project: Luge Track Comparison

(78 marks)

 

Introduction

 

This is a picture of a luge racer going down the track.

Digital Vision/Thinkstock

Luge is a winter sledding sport that was invented in Switzerland. The term luge refers to both the sport and the sled used to slide down icy tracks with plenty of curves. The riders, or sliders, lie on their backs on the sled, and use their feet and shoulders to control their movements as they go feet-first down the course.

 

In World Cup and Olympic competitions, there are single riders in both women’s and men’s events. Two-person luge events also take place.

 

All tracks in the world are designed and constructed differently. When designing a track, the primary goals are competitor safety and maximum performance. Mathematics, physics, and engineering concepts are all considered in the design.

 

Many factors contribute to the speed at which a luge athlete travels: sled aerodynamics, sled blades, clothing, boots and gloves, ice and atmosphere temperatures, athlete weight, and the track’s slope. The Whistler Sliding Centre track is considered to be the fastest in the world, but it’s also the newest course and has the most up-to-date technology. During the 2010 Olympic Winter Games, the lugers reached speeds up to 150 km/h.

 

Calgary was also host to the Winter Olympics in 1988. The Calgary luge venue was Canada Olympic Park.

 

Project Goal

 

In this project you will investigate why the luge track at the Whistler Sliding Centre is considered faster than the one at Canada Olympic Park in Calgary. The project will lead you through six steps to help you gather data and perform calculations in order to compare the two tracks. Although many factors contribute to track speed, you will focus on analyzing only the slope.

 

Timeline

 

This project is to be completed in small steps during each lesson of Module 3.

 

course folder As you complete each step, save your work to your course folder. Submit the entire project at the end of Module 3.

 

Step 1

 

At both Whistler Sliding Centre and Canada Olympic Park, there are three sports for athletes to take part in—bobsleigh, skeleton, and luge. For each sport there are different starting points along the track. The following charts provide information about each track.

 

WHISTLER SLIDING CENTRE

Track Statistics

Length (bobsleigh and skeleton)

1450 m

Length (men’s luge)

1374 m

Length (doubles and women’s luge)

1198 m

Vertical Drop

152 m

Number of Corners

16

 

CANADA OLYMPIC PARK

Track Statistics

Length (bobsleigh and skeleton)

1475 m

Length (men’s luge)

1251 m

Length (doubles and women’s luge)

1081 m

Vertical Drop

104.2 m

Number of Corners

14
  1. Slope indicates how fast one quantity changes when compared with another quantity. Using the information about the two tracks provided in the charts, describe in your own words what slope means to the sport of luge. (2 marks)

  2. All artificial luge tracks have a slope restriction for safety reasons. The average slope must be between 8% and 11%.

    For 8%, the track cannot exceed an 8-m vertical drop for every 100 m of length.

     
    This is an illustration of a right triangle with a base of 100 metres, a height of 8 metres, and a slope of eight percent.

    For 11%, the track cannot exceed an 11-m vertical drop for every 100 m of  length.

     
    This is an illustration of a right triangle with a base of 100 metres, a height of 11 metres, and a slope of 11 percent.

    Why do you think the track’s slope cannot exceed a slope of 11%? (2 marks)