Question

Planet X has a mass of 6 times the mass of Earth, and its radius is 8 times the radius of Earth. A rocket takes off from Planet X's surface, with a velocity that is 1/3 vesc, where vesc is the escape velocity of the planet. How high from the center of Planet X does the rocket reach in meters?

Answer 1

Given :

M = mass of planet X = 6*mass of earth =

R = radius of planet X = 8*radius of earth =

radius of earth =

v = velocity of projection of rocket = [ = escape velocity of the planet X]

The equation for escape velocity on surface of a planet is given by [ M = mass of planet and R = radius of planet]

Suppose the rocket reaches to a distance 'r 'from the center of the planet X.

let mass of the planet be m.

Applying Conservation of Mechanical Energy for the rocket at surface of the planet and to the distance 'r' :

Potential energy at the surface + Kinetic energy = Potential energy at distance r

[answer]