Logan, with mass m = 75 kg, is standing at the eage
of a dock holding onto a rope with length, L. = 4.0 m, which is suspended from a tree branch above. The rope is taut and makes an angle, 0, of 30° with the ver- tical direction. Logan very gently steps off of the dock and swings in a circular are until he releases the rope when it makes an angle, d, of 12° with the vertical,
but on the other side of the branch. a. Define your system so that you may use it to complete the rest of this problem, and construct a diagram showing the initial (i) and final (f) configu-
rations of Logan's swing. b. Apply the principle of energy conservation to the system in terms of K, K,, U, and U, in terms of
0, Ф, L, g, m, v, and v.. c. Evaluate the expression in part (b) to determine
Logan's speed when he releases the rope. d. Justify the selection of additional data required to determine the horizontal displacement of Logan from the edge of the dock to when he strikes the water and summarize the mathematical model from which the displacement can be
calculated.