Question

Obtain the equations that describe the motion of a body thrown vertically at a speed greater than the escape velocity. Discount air resistance.

Answer 1

escape velocity is defined in terms of kinetic energy, because it is often easier to work with because it is not a vector.

so mgh = .5mv^2 = GmM/r^2 ++ just using the height dependent form of g

ten v^2 = 2GM/r^2
or V = SqrRoot[ 2GM ] /r

The object must have greater energy than its gravitational binding energy to escape the earth's gravitational field. So:

1/2 mv2 = GMm/R

Where m is the mass of the object, M mass of the earth, G is the gravitational constant, R is the radius of the earth, and v is the escape velocity. It simplifies to:

v = sqrt(2GM/R)

the motion can be seen like this

cited from the link the image ---//img.wizedu.com/questions/d19a9480-04c2-11ef-8b05-97aaa69b19fb.gif?x-oss-process=image/resize,w_580

cited the image fom the link --http://www.boredofstudies.org/wiki/images/f/f6/Sci_phys_space_escape_velocity.png