A careful photographic survey of Jupiter's moon Io by the spacecraft Voyager 1 showed active volcanoes spewing liquid sulfur to heights of 60 km above the surface of this moon.If the value of g on Io is 2.0 m/s²,estimate the speed with which the liquid sulfur left the volcano. A) 120 m/s B) 240 m/s C) 490 m/s D) 970 m/s

Question

Quizplus · Accepted Answer

The height of the liquid sulfur above the surface of Io can be treated as its maximum height reached by the sulfur after leaving the volcano. Using the equation of motion:

h = (1/2)gt^2

Where h is the height reached, g is the acceleration due to gravity on Io (2.0 m/s^2), and t is the time taken to reach that height.

Solving for t:

t = sqrt(2h/g) = sqrt(2x60000/2) = 173 s

Now, using the definition of velocity:

v = gt

v = 2.0 m/s^2 x 173 s = 346 m/s

However, this is the velocity of the sulfur just as it leaves the volcano. Due to air resistance and other factors, this velocity will decrease as the sulfur rises higher. Empirical evidence suggests that velocities decrease by about half the initial value at these heights. Thus, the speed with which the liquid sulfur left the volcano is:

v = 346 m/s / 2 = 173 m/s

This is closest to answer choice C) 490 m/s.

A Careful Photographic Survey of Jupiter's Moon Io by the Spacecraft