Question

Several volcanoes have been observed erupting on the surface of one of Jupiter's closest moons. Suppose that material ejected from one of these volcanoes reaches a height of 5.10 km after being projected straight upward with an initial speed of 132 m/s. Given that the radius of this particular moon is 2000 km, calculate its mass. (in kg)

Answer 1

Answer: 1.025*10^23 kg

Step-by-step explanation:

Given

Height of eruption, h = 5.1 km

Initial speed of the material, v = 132 m/s

Radius of moon, r = 2000 km

Mass of the moon, m = ?

We would solve this by using the formula

g = GM/r²

Also, we know that

h = v²/2g, substituting the formula of g into this equation, we have

h = v²/2(GM/r²)

h = v²r² / 2GM

Since we are looking for the mass, we make m the subject of formula, so that

M = v²r² / 2Gh

Now, substituting all the values, we get

M = [132² * (2000*10^3)²] / 2 * 6.67*10^-11 * 5.1*10^3

M = (17424 * 4*10^12) / 6.8*10^-7

M = 6.97*10^16 / 6.8*10^-7

M = 1.025*10^23 kg

Thus, the mass of the moon is 1.025*10^23 kg