Answer
$v = 0.65~m/s$
Work Step by Step
We can find the period for a full swing as:
$T = 2\pi~\sqrt{\frac{L}{g}}$
$T = 2\pi~\sqrt{\frac{0.90~m}{9.80~m/s^2}}$
$T = 1.9~s$
Since it is only half a swing from one handhold to the next, the time from one handhold to the next is $\frac{T}{2}$ which is $0.95~s$.
We can find the amplitude of the motion as:
$\frac{A}{L} = sin(\theta)$
$A = L~sin(\theta)$
$A = (0.90~m)~sin(20^{\circ})$
$A = 0.31~m$
Since the distance from one handhold to the next is $2A$, the distance from one handhold to the next is 0.62 meters.
We then find the speed of forward motion;
$v = \frac{distance}{time}$
$v = \frac{0.62~m}{0.95~s}$
$v = 0.65~m/s$
