Answer:
91.5 km
Explanation:
Hi!
If we are to ignore the variation in gravity we can use the formula for teh potential energy near the surface of a planet:
mgh
If the energy of the material ejected from the volcano on Io's surface is the same on earth's surface we have:
[tex]mg_{Io}h_{Io} =mg_{e}h_{e}[/tex]
where subindexes Io and e means Jupiter's moon Io, and Earth, respectively
solving for h_e
[tex]h_{e} = h_{Io} \frac{g_{e}}{g_{Io}}[/tex]
The acceleration due to the gravity of a planet can be calculated as:
[tex]g = G \frac{m}{R^2}[/tex]
Where R and m are the radius and mass of the planet
Therefore:
[tex]h_{e} = h_{Io} (\frac{m_{Io}}{m_e})(\frac{R_e}{R_{Io}})^2[/tex]
m_e = 5,972 × 10^24 kg
R_e = 6 371 km
Replacing all given values:
h_e = 500 km *(0.183) = 91.515 990 km