Question

Astronomers have discovered several volcanoes on io, a moon of jupiter. one of them, named loki, ejects lava to a maximum height of 2.00 â 105 m. suppose another volcano on a different moon ejected lava at a height of 1.89 â 105 m where the acceleration of gravity is 1.72 m/s2.

Answer 1

The question seems to be incomplete. However, I can think of a possible logical question this problem could have. The equation for the maximum height attained by any object thrown upwards is:

H = v²/2g

I think the question would be determining the gravity in Io assuming that the initial velocity of the lava is the same. Then, the solution is as follows:

Let's use the other volcano to find v.
1.89×10⁵ m = v²/2(1.72 m/s²)
Solving for v,
v = 806.325 m/s

So, we use this to find g in Io.
2×10⁵ m = (806.325)²/2(g)
Solving for g,
g = 1.6254 m/s²