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DYNAMICS - CASE STUDY

    Introduction


 

A cargo plane has to drop a relief package to people in need. How can the pilot determine when to drop the package?

What is known:

  • The plane is flying level (vertical velocity = 0) at 600 ft.
  • The plane is traveling at 176 ft/s in a straight line toward the drop target.
  • The wind resistance on the package can be neglected.
     
    Question


Problem Diagram

 

When releasing the package, at what angle θ down from the horizontal must the pilot see the target for the package to land on the target?

   
  Approach

 
  • Use vectors to analyze curvilinear motion.
  • Resolve the vectors for curvilinear motion into rectangular components.
  • Integrate the acceleration to find the horizontal distance covered by the package, then use trigonometry to determine the angle θ.
     
   
 
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