Question

Io, a satellite of Jupiter, is the most volcanically active moon or planet in the solar system. It has volcanoes that send plumes of matter over 500 km high. Due to the satellite's small mass, the acceleration due to gravity on Io is only 1.81 m/s2, and Io has no appreciable atmosphere. Assume that there is no variation in gravity over the distance traveled. Part A What must be the speed of material just as it leaves the volcano to reach an altitude of 490 km

Answer 1

Answer:

1.33 km/s

Explanation:

acceleration due to gravity, g = 1.81 m/s²

height, h = 490 km = 490000 m

Let u is the initial speed and the final speed is zero.

use third equation of motion

v² = u² - 2 g h

0 = u² - 2 x 1.81 x 490000

u² = 1773800

u = 1331.84 m/s

u = 1.33 km/s

Thus, the initial speed of the material is 1.33 km/s.

Answer 2

Answer:

1331.84 m/s

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity = 0

s = Displacement = 490 km

a = Acceleration

g = Acceleration due to gravity = 1.81 m/s² = a

From equation of linear motion

$v^2-u^2=2as\\\Rightarrow -u^2=2as-v^2\\\Rightarrow u=\sqrt{v^2-2as}\\\Rightarrow u=\sqrt{0^2-2\times -1.81\times 490000}\\\Rightarrow u=1331.84\ m/s$

The speed of the material must be 1331.84 m/s in order to reach the height of 490 km