Question

. You read in the newspaper that rocks from Mars have been found on Earth. Your friend says that

the rocks were shot off Mars by the large volcanoes there. You are skeptical so you decide to

calculate the magnitude of the velocity that volcanoes eject rocks from geological evidence. You

know the gravitational acceleration of objects falling near the surface of Mars is only 40% that on

the Earth. You can look up the height of Martian volcanoes and determine the distance rocks from

a volcano hit the ground from pictures of the Martian surface. If you assume the rocks farthest

from a volcano were ejected at an angle of 45 degrees, what is the magnitude of the rock's

velocity as a function of its distance from the volcano and the height of the volcano for the rock

furthest from the volcano?

Answer 1

Let's assume that gravitational acceleration is constant during the whole motion, and the origin of the movement is at the crater of the volcano. The motion can be described using equations of free fall and with the diagram below:

Motion in x direction:

Motion in y direction:

Reeplacing t in y motion equation:

Another equation involved in vertical motion is:

The magnitude of the velocity is the square root of the sum of square components. Then:

Reeplacing the value of initial velocity:

The rock furthest from the volcano is located at y = - h (when it hits the ground), where h is the height of the volcano. Then, using an angle of 45°, and a 40% Terrestial graviational acceleration: