For a piece of volcanic ejecta thrown with velocity v at anangle to the horizont

Question

For a piece of volcanic ejecta thrown with velocity v at anangle to the horizontal, we conclude that thehorizontal range is (v2sin2)/g and the max hieghtis (v2sin2)/2g Given that sulfur fountains on Io reach an altitude of atleast 400 km, calculate the speed at which they erupt. For a piece of volcanic ejecta thrown with velocity v at anangle to the horizontal, we conclude that thehorizontal range is (v2sin2)/g and the max hieghtis (v2sin2)/2g Given that sulfur fountains on Io reach an altitude of atleast 400 km, calculate the speed at which they erupt.

Explanation / Answer

like above, h=(v2sin2)/2g 2gh=v2sin2 v2=2gh/sin2 v=(2gh/sin2) Remember that is is on Io, so you need to find the acceleration dueto gravity there, which turns out to be 0.028 m/s2 Also, notice 400 is in kilometers, so you need to convert itto meters. v=(2gh/sin2)=(2*0.028*400000/sin2)=(2240/sin2) If you decide to use =90o, thensin2 is 1, and v=(2240/1)=(2240)=47.329 m/s If it didn't launch vertically, you need to know the angle.

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