The material will go as high as 91.54 km would this material go on earth if it were ejected with the same speed as on Io.
The height of the material on earth will be derived from the given values as follows:
Tue acceleration due to gravity on Io, go is given as:
[tex]g_o = \frac{GM}{r^{2}}[/tex]
Substituting the values:
[tex]g_o= \frac{6.67×10^{-11}×8.93×10^{22}}{1821000^{2}}[/tex]
[tex]g_o = 1.796 m/s^{2}[/tex]
Height on earth, He and Height on Jupiter H is given as follows:
[tex]H_e = \frac{v^{2}}{2g}[/tex]
[tex]H = \frac{v^{2}}{2g_o}[/tex]
Taking ratio of the two heights and solving for height on earth, He:
[tex]H_e = H × \frac{g_o}{g}[/tex]
Substituting the values:
[tex]H_e = 500000 × \frac{1.796}{9.81} = 91539.245 m[/tex]
Therefore, the material will go as high as 91.54 km would this material go on earth if it were ejected with the same speed as on Io.
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