23 01 2018



Congratulations!  You have just been hired as a Marketing Assistant for Meier Skis in Denver, Colorado. Meier Skis makes high-performance, hand-crafted skis and snowboards with respect for the environment.  The company is gaining recognition as a US-based company that is eco-friendly and environmentally conscious using locally sourced materials from small businesses when possible.  To generate business, the company is offering factory tours.  You have been asked to talk about the various types of skiers and snowboarders who buy Meier products:  beginner/recreational, intermediate/advanced, and slalom racers.  Your research department has collected some data at an indoor ski dome in Germany and is looking to you to model the ski tracks and discuss your models.

You decorated the conference room with the following pictures to use as reference:








In order to be taken seriously, you must prepare some models in Desmos using the data from your research team.  YOU MAY NOT USE THE REGRESSION FEATURE OF YOUR CALCULATOR OR DESMOS; ALL EQUATIONS MUST BE GENREATED BY YOU!  Further instructions are on your paper.  GOOD LUCK!

Fraction of a Turn Left Ski Position (inches)
0.0 6
0.5 132
1.0 6
1.5 -120
2.0 6



Plane Rescue

15 01 2018


(Group Task)

SCENARIO:  As a Search and Rescue Park Ranger in Yellowstone National Park, you have been assigned to help in rescue efforts to locate a downed private airplane.  Unfortunately, the plane crashed in a densely forested section of the park.  A witness (W), located due east of the Ranger Station (S), saw the plane (P) go down.  Smoke can be seen rising above the trees.  You, the ranger (R), are presently due west of the location of the witness (W).

TASK:  Find an R location in the gym not being used by another group.  Record your given information on your paper.  Look diagonally across the park (gym); you should see the plane or the smoke from the crash.  Continue all work on your paper.


SW (miles)

RW (miles)

RC (miles)

CZ (miles)


14 TBD 4 1







14 TBD 3



14 TBD 4 0.5


14 TBD 2


#6 14 TBD 2



Flight School

14 01 2018

(Group Task)

SCENARIO:  You are taking an exam for your pilot’s license for which you need to determine the speed and direction of the airplane given the wind speed/direction and resultant ground speed/direction.


You are assigned Virgin Airlines Flight VX1352 en route from San Francisco to Boston.  Follow the directions and record your answers on your test paper.


  1. Using a flight tracking software you collect the following data while you track the plane for several minutes.The direction angle given is a true compass bearing and not a directional bearing relative to a North-South line. Use a GPS distance calculator to determine the distance between the starting point at 05:30:56 PM and ending point at 05:35:32 PM.  A recommended utility is:
    Express the distance in miles.  NOTE:  There are 1.61 km in a mile.
  2. Determine what state the plane is flying over.
  3. Determine the total time elapsed MM:SS in the boxed in area.
  4. Determine the plane’s ground speed in mph.
  5. Express the plane’s ground speed (resultant vector) in component form.Vx3mod
  6. You look up the wind speed/direction in the plane’s location.NOTE: The wind direction angle is a true compass bearing while the letters indicate the direction the wind is coming from. For instance, a wind direction of 270° W means a wind blowing directly to the east.  Express the wind vector in component form.
  7. Determine the airplane speed vector in component form.
  8. Express the airplane speed in mph and its direction using a directional bearing relative to a North-South line.


Stepping Stones Puzzle

14 01 2018

logoCongratulations on being chosen as a finalist for a summer internship with GKN Aerospace in Cromwell, CT.  All of the candidates are highly qualified and deserving.

Group of 2:  You will need only one paper for the pair of you.  In order to earn your spot on the team, you and your partner will have to complete a stepping stones puzzle by correctly solving trigonometric equations.  You will need to divide up the work evenly between you by alternating problems.  If you get stuck and your partner needs to complete two in a row, then you will have to do the next two in a row so that you have an even distribution of your work.  WRITE YOUR INITIALS IN EACH SQUARE YOU DO.

Group of 3:  You will each need an individual sheet.  In order to earn your spot on the team, your group will have to complete a stepping stones puzzle by correctly solving trigonometric equations.  You will all be simultaneously working on the problems and compare/discuss/agree before moving on.  WRITE YOUR NAME on the paper.


  • All problems are on the interval [0, 2π).
  • You may only advance one problem at a time.
  • Place a cone on top of the problem once you have solved it.
  • Show your work on the paper provided in the grid corresponding to the puzzle problem you are solving.
  • Take a picture of the completed puzzle with cones indicating the path you took and email the photo to your teacher.  (One photo per group.)
  • Once you take the photo, remove and stack the cones.
  • Turn in your work to your teacher.

Accident-Scene Analysis

4 01 2018


Welcome to the Connecticut Police Academy where today we will evaluate your skills in documenting and analyzing the scene of a motor vehicle accident.  GOOD LUCK!


Police are trained in accident-scene analysis.  One of the things they need to do is determine skid marks from yaw marks and then they need to create a sketch of the marks.

Yaw marks (A through E  below) are what’s left by a tire that is still rolling but is simultaneously sliding laterally. They are always curved and initiated by a steering input. If you’re driving too fast into a corner you’ll create a set of yaw marks. Yaw marks have distinct striations, stripes or streaks induced as the sidewall is dragged over the road. These marks are aligned in the direction of the spin, usually parallel to the car’s axle.

A skid mark (E to F below) is defined as a tire mark on asphalt surface produced by a tire that is not rotating and follow a straight path.  Skid marks are generally faded at the beginning and get heavier as they continue.

For yaw marks, police officers typically construct a chord across the arc and measure its length; then they measure the radius from the highest point to the chord.  For skid marks, they measure the length as well as the starting and ending relative points.  All of this data can be used in a court of law.


IMPORTANT:  Measure in inches for this task.  Further instructions are on your paper.

Bike Frame Geometry

4 01 2018

PERFORMANCE TASK (Individual Task)



Congratulations on your new position with Watson Cycles in Waterford, CT.  Watson Cycles was created by Andrew Watson; the company builds small custom bicycle frames with a focus on American-made materials.  Your boss has heard that Cannondale will reveal its newest model frame at a trade show in Hartford.  Although Cannondale’s model will most likely be made from carbon fiber, your boss remains undaunted since his custom aluminum, titanium, and steel frames fill a niche between entry-level frames and high-end carbon-fiber frames.  Nonetheless, he has sent you to discreetly measure the Cannondale frame so your design group can begin the reverse-engineering process immediately upon your return.    Although you do your best, the Cannondale representatives are wise to your intentions and ask you to leave before you are done; you are a few measurements short of your goal.  Your job security depends on your ability calculate the following to the nearest hundredth:

  1. Length of seat stay
  2. Angle between seat stay and chain stay
  3. Angle between seat stay and seat tube
  4. Length of down tube
  5. Angle between seat tube and down tube
  6. Angle between seat tube and top tube

The rest of the information you need is on paper.

Paper Plate Activity

26 02 2017