Question

A rope of length L is attached to a support at point C. A person of mass m₁ the other end of the rope so that it is horizontal and taut, as shown. The person then drops off the ledge sits on a ledge at position A holding and swings down on the rope toward position B on a lower ledge where an object of mass m₂ is at rest. At object then land together in the lake at point D, which is a vertical distance L below position B. Air resistance and the mass of the rope are negligible. Derive expressions for each of the following in terms of m₁, m₂ L, and g.

(a) The speed of the person just before the collision with the object position B the person grabs hold of the object and simultaneously lets go of the rope. The person and  

(b) The tension in the rope just before the collision with the object

(c) The speed of the person and object just after the collision

(d) The total horizontal displacement x of the person from position A until the person and object land in the water at point D.

Answer 1

   

The dx found is measured from the edge of the second lower cliff so the total horizontal distance would have to include the initial x displacement (L) starting from the first cliff.