# 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.