Answer:
91.54 km
Explanation:
G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²
r = Radius of Io = 1821000 m
m = Mass of the Io = 8.93 × 10²² kg
[tex]H_i[/tex] = 500000 m
g = Acceleration due to gravity on Earth = 9.81 m/s²
Acceleration due to gravity on Io
[tex]g_i=\frac{GM}{r^2}\\\Rightarrow g_i=\frac{6.67\times 10^{-11}\times 8.93\times 10^{22}}{1821000^2}\\\Rightarrow g_i=1.796\ m/s^2[/tex]
[tex]H_e=\frac{v^2}{2g}[/tex]
[tex]H_i=\frac{v^2}{2g_l}[/tex]
Dividing the above equations we get
[tex]\frac{H_e}{H_i}=\frac{\frac{v^2}{2g}}{\frac{v^2}{2g_i}}\\\Rightarrow \frac{H_e}{H_i}=\frac{g_i}{g}\\\Rightarrow \frac{H_e}{H_i}=\frac{1.796}{9.81}\\\Rightarrow H_e=H_i\times \frac{1.796}{9.81}\\\Rightarrow H_e=500000\times \frac{1.796}{9.81}\\\Rightarrow H_e=91539.245\ m=91.54\ km[/tex]
The material would go 91.54 km on earth if it were ejected with the same speed as on Io.
