## College Physics (4th Edition)

Tarzan's initial speed should be at least $5.8~m/s$
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 $5.8~m/s$.