Motion of the Rowboat

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.

• 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