Answer
Tarzan's initial speed should be at least $5.8~m/s$
Work Step by Step
Let $h_1$ be the original height. Let $h_2$ be the height of the higher ground across the gully. We can assume that the final speed is zero. We can use conservation of energy to find the initial speed $v_1$:
$mgh_1 + \frac{1}{2}mv_1^2 = mgh_2$
$\frac{1}{2}mv_1^2 = mg~(h_2-h_1)$
$v_1^2 = 2g~(h_2-h_1)$
$v_1 = \sqrt{2g~(h_2-h_1)}$
$v_1 = \sqrt{(2)(9.80~m/s^2)(1.7~m)}$
$v_1 = 5.8~m/s$
Tarzan's initial speed should be at least $5.8~m/s$.
