I On the earth, an astronaut can safely jump to the ground from a height of \(1.0 \mathrm{~m}\); her velocity when reaching the ground is slow enough to not cause injury. From what height could the astronaut safely jump to the ground on the moon?

A. \(2.4 \mathrm{~m}\)

B. \(6.0 \mathrm{~m}\)

\(\begin{array}{ll}\text { C. } 7.2 \mathrm{~m} & \text { D. } 36 \mathrm{~m}\end{array}\)

\(\begin{array}{ll}\text { C. } 7.2 \mathrm{~m} & \text { D. } 36 \mathrm{~m}\end{array}\)

Objects in free fall on the earth have acceleration \(a_{y}=-9.8 \mathrm{~m} / \mathrm{s}^{2}\). On the moon, free-fall acceleration is approximately \(1 / 6\) of the acceleration on earth. This changes the scale of problems involving free fall. For instance, suppose you jump straight upward, leaving the ground with velocity \(v_{\mathrm{i}}\) and then steadily slowing until reaching zero velocity at your highest point. Because your initial velocity is determined mostly by the strength of your leg muscles, we can assume your initial velocity would be the same on the moon. But considering the final equation in Synthesis 2.1 we can see that, with a smaller free-fall acceleration, your maximum height would be greater. The following questions ask you to think about how certain athletic feats might be performed in this reduced-gravity environment.