The first active volcano observed outside the Earth was discovered in 1979 on Io, one of the moons of Jupiter. The volcano was observed to be ejecting material to a height of about 2.40 ✕ 105 m. Given that the acceleration of gravity on this moon is 1.97 m/s2 find the initial velocity of the ejected material.

Question

anonymous · Answer

$$2.4*10^{5}$$ is what it is supposed to be for the height btw

anonymous · Answer

I assumed as much. I'm an astrophysics major, I've got a rough idea about the scaling of these types of phenomena.

Kinematic equation: Vf^2 = Vi^2 + 2a(Xf - Xi)

In this case, Vf will be 0, because there is a max height where it will come to a stop before accelerating back down towards the surface of the moon.

We'll take Xi to be 0 as well, since the height of a volcano is probably minimal compared to 10^5 m.

a is just the acceleration, but we have to remember it is negative here since it opposes motion!

0 = Vi^2 - (2)(1.97)(2.4 x 10^5 - 0)
Vi = sqrt(2 * 1.97 * 2.4x10^5) = sqrt(9.456 x 10^5) = 9.72 x 10^2

So, the initial velocity would be 972 m/s I believe.

anonymous · Answer

Thank you so much! I used that equation I just messed up one of my signs. So I had a plus sign instead of a minus sign and it threw me off.