Several volcanoes have been observed erupting on the surface of Jupiters closest

Question

Several volcanoes have been observed erupting on the surface of Jupiters closest moon, Io. Suppose that material ejected from one of these volcanoes reaches a height of 5.60 km after being projected straight upward with an initial speed of 205 m/s. (a) Given that the radius of Io is 4029 km, outline a strategy that allows you to calculate the mass of Io. This answer has not been graded yet. (b) Use your strategy to calculate Io's mass. kg + -2 points Walker2 12.P013. My Notes Ask Your (a) Find the acceleration of gravity on the surface of Mars. m/s2 (b) Find thacceleration of gravity on the surface of Venus. m/s2 Submit Assignment Save Assignment Progress Home My Assignments Extension Reques

Explanation / Answer

a)

vi=205m/s, hmax=5.60*10^3 m

At maximum height, vf= 0 m/s

Apply kinematic eqn,

vf^2=vi^2+2*a*hmax

0^2=205^2+2*a*5600

a=-3.75m/s^2

Now use gravitational law,

Weight of the object = Gravitational force on a object on the surface moon

mg=GMm/r^2

Where m=mass of the object, M=mass of the moon, r=radius of the moon, gtavity on the moon=a=-3.75m/s^2

g=GM/r^2

M=gr^2/G----------------(1)

b)

Plugging values in eqn (1),

M=[3.75*4029*10^3)^2]/(6.67*10^-11)

M=9.12*10^23 kg

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