Jupiter's moon io has active volcanoes (in fact, it is the most volcanically active body in the solar system) that eject material as high as 500 km (or even higher) above the surface. io has a mass of 8.93×1022kg and a radius of 1821 km. for this calculation, ignore any variation in gravity over the 500 km range of the debris. how high would this material go on earth if it were ejected with the same speed as on io?

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

= 500000 m

g = Acceleration due to gravity on Earth = 9.81 m/s²

Acceleration due to gravity on Io

Dividing the above equations we get

The material would go 91.54 km on earth if it were ejected with the same speed as on Io.

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.