# Problem 7-51 Energy cons. - Part 8 - A

A boy is playing with a rope tied to a tree near his favourite swimming hole. Initially the boy is stationary and the rope (of length \(3.7 \;m\)) makes an angle of \(48^\circ\) with the vertical. He then lifts his feet slightly and starts to swing freely. If air resistance is neglected, use conservation of energy to determine:

(a) his speed at the bottom of the swing

(b) the minimum height, relative to his initial position, to which he can swing.

**Accumulated Solution**

At point 2, \(E_P = 0\)

At point 2, \(E_K = (1/2)mv^2\)

\(h = 3.7(1 - \cos48) \;m = 1.22 \;m\)

E at point \(1 = 0 + mgh\)

E at point \(2 = (1/2)mv{_2}{^2} + 0\)

\(v_2 = 4.9 \;m/s\) (answer to part (a))

Correct.

He would rise to his original height. (answer to part (b))

**You have completed this problem.**