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MATHEMATICS - CASE STUDY

    Introduction


Motion of the Rowboat
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Location of the Stone

 


 

In a park, a boat is initially stayed beside the pier by a rope of length L at point A (the rope is loose). The the wind blows the boat to point B (the rope is straight and tout). The worker needs to pull the boat to the end of the pier (point C) to load people. A big stone is located at point D. The worker walks along the pier from point A toward point C and pulls the rowboat by the rope with him. During the pulling, the man keeps the rope straight and tout.

 What is known:

  • The length of the rope is L = 20 m.  
  • The distance from A to C is S = 50 m.
  • The stone located at point D which is  5 m from the pier and 25 m from the bridge.
  • Neglect the size of the stone and the rowboat. 
  • Rope is not pulled in until the man reaches the end of the pier.
   
  Questions

  Determine if the boat will collide with the stone.
   
  Approach

 
  • Since the man pulls the boat by a rope which is straight and tout, the path followed by the boat will be a curve and the rope will always be tangent to the curve.
  • After the man arrives the bridge, he stands there to pull the boat to the bridge.
  • Consider trigonometric substitutions