Answer
The speed at the bottom of the swing is $8.42~m/s$
Work Step by Step
We can find the difference in height between the starting point and the bottom of the swing:
$h = (20.0~m)-(20.0~m)~cos~35.0^{\circ} = 3.62~m$
The kinetic energy at the bottom will be equal to the magnitude of the change in the potential energy:
$\frac{1}{2}mv^2 = mgh$
$v = \sqrt{2gh}$
$v = \sqrt{(2)(9.80~m/s^2)(3.62~m)}$
$v = 8.42~m/s$
The speed at the bottom of the swing is $8.42~m/s$.
