Assessment Task:
Science and Maths Report Writing Assessment Answer

The Escaped Robotic Bees

Buzz labs have built a prototype of robotic bees. They are still in early stages of development and they will immediately sting any person they come in to contact with
Two bees are running loose in the labs and are heading straight towards the engineers. They have two ways to stop the bees before being stung: hitting them with a laser beam or hitting them with a disabling sonic blast.

In this investigation you will use vectors to represent the position and velocity of the two robotic bees in 3-dimensional space. Considering two bees, A and B, set up the following:

  1.  Bee A has initial position and has velocity vector .
  2.  Bee B has initial position and has velocity vector .

In this investigation, using varying initial positions and velocity vectors for your bees, you investigate the location and speed of the bees and the distance they are apart.
In addition, you need to determine the best position and time to use the laser beam and sonic blaster to disable the bees. You will model your scenarios with 3D graphing software.

PART 1
Sensibly choose the initial positions and velocity vectors of your bees. You must ensure that:

  1.  The speed of each bee is within a realistic range
  2.  The motion of the bees are not parallel or coincident to each other
  3.  The shortest distance between the two bees does not occur when t = 0

You will create a minimum of 2 scenarios for the velocities of the bees: one where they are coplanar and one where they are skew. For your chosen values find the parametric equations for the position of each bee at time t, where t is the time in seconds, using centimetres for the distance. What is the speed of each bee and how long does it take each bee to reach an engineer at a point of your choice along its straight-line path?

PART 2
If at time t, bee A is at position P and bee B is at position Q, determine the vector PQ and find their distance apart at any instant. Find the time when the bees are closest to each other and their distance apart at this instant.

PART 3
Laser Beam:
Now investigate the best location and time for the laser beam to hit both bees with one shot. The laser beam may be represented by a line in 3D, or a vector.
Sonic Blaster: Also investigate the best location and time for a sonic blaster to hit both bees in one shot. Add the blast to your 3D model. Now come up with your own method/s on how to disable/stop the two bees and include it in your 3D model. Be as creative as you like.

PART 4
Analyse and interpret your results, including consideration of the reasonableness and limitations of the results. Describe and discuss any assumptions you have made. Using Gegebra, or some other 3D modelling software, develop a graphical representation of the motion of the bees, laser beams, sonic blaster, engineers and any other factors you have included. Complete a report for the mathematical investigation.

The investigation report should be a maximum of 15 single-sided A4 pages if written, or the equivalent in multimodal form.

The report may take a variety of forms, but would usually include the following:

  1.  an outline of the problem and context
  2.  the method required to find a solution, in terms of the mathematical model or strategy used
  3.  the application of the mathematical model or strategy, including

– relevant data and/or information
– mathematical calculations and results, using appropriate representations
– the analysis and interpretation of results, including consideration of the reasonableness and limitations of the results

  •  the results and conclusions in the context of the problem.

A bibliography and appendices, as appropriate, may be used. The format of an investigation report may be written or multimodal. The report, excluding bibliography and appendices if used, must be a maximum of 15 A4 pages if written, or the equivalent in multimodal form. The maximum page limit is for single-sided A4 pages with minimum font size 10. Page reduction, such as 2 A4 pages reduced to fit on 1 A4 page, is not acceptable. Conclusions, interpretations and/or arguments that are required for the assessment must be presented in the report, and not in an appendix. Appendices are used only to support the report, and do not form part of the assessment decision.

 

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  • Uploaded By : Mitchell Lee
  • Posted on : November 21st, 2018

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