Question

The first active volcano observed outside the earth was discovered in 1979 on io, one of the moons of jupiter. suppose a volcano on another moon is observed to be ejecting material to a height of about 1.52 ✕ 105 m. given that the acceleration of gravity on this moon is 1.91 m/s2 find the initial velocity of the ejected material.

Answer 1

Gravitation due to the planet's mass is always against the ejected particle velocity. This will result in deceleration of the ejected particle and eventually bring the velocity to zero at the topmost point of the trajectory before pulling it back to the ground.

By the kinematic equation

$v^2 - u^2 = 2.a.s$

where s is the distance travelled = 1.52 x 10^5 m

a is the acceleration due to gravity = -1.91 m/s^2

v and u are initial and final velocities, so v = 0.

Therefore

$u = \sqrt{s.a.s}$

u = 761.99 m/s