Answer
The speed is $~~1.4~m/s$
Work Step by Step
We can find the height $h_1$ above the lowest point when the angle is $30.0^{\circ}$:
$\frac{L-h_1}{L} = cos~\theta$
$L-h_1 = L~cos~\theta$
$h_1 = L~(1-cos~\theta)$
$h_1 = (1.4~m)~(1-cos~30.0^{\circ})$
$h_1 = 0.19~m$
We can find the height $h_2$ above the lowest point when the angle is $20.0^{\circ}$:
$\frac{L-h_2}{L} = cos~\theta$
$L-h_2 = L~cos~\theta$
$h_2 = L~(1-cos~\theta)$
$h_2 = (1.4~m)~(1-cos~20.0^{\circ})$
$h_2 = 0.084~m$
We can use conservation of energy to find the speed:
$K_2+U_2 = K_1+U_1$
$K_2 = 0+U_1-U_2$
$\frac{1}{2}mv_2^2 = mg~(h_1-h_2)$
$v_2^2 =2g~(h_1-h_2)$
$v_2 =\sqrt{2g~(h_1-h_2)}$
$v_2 =\sqrt{(2)(9.8~m/s^2)(0.19~m-0.084~m)}$
$v_2 = 1.4~m/s$
The speed is $~~1.4~m/s$
