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Problem Title: The Drug Runner Problem

     
  Year: 1988      
  Student Level: Undergraduate      
  Source: MCM      
  Commentary: No      
  Student Papers: No      
     
  Problem  
 

Two listening posts 5.43 miles apart pick up a brief radio signal. The sensing devices were oriented at 110º and 119º, respectively, when the signal was detected (see Figure 1); and they are accurate to within 2º. The signal came from a region of active drug exchange, and it is inferred that there is a powerboat waiting for someone to pick up drugs. It is dusk, the weather is calm, and there are no currents. A Small helicopter leaves a pad from Post 1 and is able to fly accurately along the 110º angle direction. The helicopter's speed is three times the speed of the boat. The helicopter will be heard when it gets within 500 ft of the boat. This helicopter has only one detection device, a searchlight. At 200 ft, it can just illuminate a circular region with a radius of 25 ft.


Figure 1: Geometry of the problem.

  • Describe the (smallest) region where the pilot can expect to find the waiting boat.
  • Develop an optimal search method for the helicopter. Use a 95% confidence level in your calculations.
 
         
  Commentary      
 

None

 
 
         
  Student Papers      
 

None