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8 December, 16:03

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)

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  1. 8 December, 17:32
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    Answer: 1.025*10^23 kg

    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
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