## Question:

A tugboat T having mass ${ m }_{ T }$ is tied to a barge B having mass ${ m }_{ B }$. If the rope is “elastic” such that it has stiffness k, determine the maximum stretch in the rope during the initial towing. Originally both the tugboat and barge are moving in the same direction with speeds ${ v }_{ T1 }$ and ${ v }_{ B1 }$ respectively. Neglect the resistance of the water. Units Used: Mg = ${ 10 }^{ 3 }$ kg , kN = ${ 10 }^{ 3 }$ N Given: ${ m }_{ T }$ = 19 Mg , ${ v }_{ B1 }$ = 10 km/hr , ${ m }_{ B }$ = 75 Mg , ${ v }_{ T1 }$= 15 km/hr , k = 600 kN/m , g = ${ 9.81 m/s }^{ 2 }$