Moon jump height

A safe jump is considered to be one in which a person hits the ground at a maximum speed of 8 m/s. Determine the maximum height from which jumping and landing on the moon is safe. The acceleration on the earth is g= 10 m/s², and the acceleration on the moon is 6 times smaller than on the earth.

Final Answer:

h₁ =  3.2 m
h₂ =  19.2 m

Step-by-step explanation:

$$\begin{gathered} v=8\text{m/s} \\ {g}_1=10{\text{m/s}}^2 \\ {g}_2=g_1/6=10/6=\frac{5}{3}\doteq 1.6667{\text{m/s}}^2 \\ {g}_1=v/t_1 \\ {g}_2=v/t_2 \\ {t}_1=v/g_1=8/10=\frac{4}{5}=0.8\text{s} \\ {t}_2=v/g_2=8/1.6667=\frac{24}{5}=4.8\text{s} \\ {h}_1=\frac{1}{2}\cdot g_1\cdot t_1^2=\frac{1}{2}\cdot 10\cdot 0.8^2=3.2\text{m} \end{gathered}$$

$h_2=\frac{1}{2}\cdot g_2\cdot t_2^2=\frac{1}{2}\cdot 1.6667\cdot 4.8^2=19.2\text{m}$

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