# Gravitation or Mechanics?

#### zorro

1. The problem statement, all variables and given/known data
A particle is projected from the surface of the earth with an initial speed of 4km/s. Find the max. height attained by the particle. Radius of earth = 6400 km and g=9.8 m/s2

2. Relevant equations

3. The attempt at a solution

I have two approaches to this problem.

1)Mechanics-
Since gravitational force is conservative, we have
0.5mv2 = mgh
On solving, h = 816 km

2)Gravitation-
On the surface of earth, gravitational potential energy is -gmr , where m is the mass of the body and r is the radius of earth.

At a height h, its potential energy is -gmr2/(r+h)
0.5mv2 - gmr = -gmr2/(r+h)
h=Rv2/(2gr-v2)
On solving, h = 935 km

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

#### The legend

since the initial velocity is high the object is going to reach a very high spot... And at such heights there's a 'effective' change in g. So your mechanics approach would be wrong as the acceleration would be variable.

#### The legend

i think you have to include this change in g in your gravitational approach too..

#### zorro

Thanks dude! I got it,
in gravitational approach the change in accln. due to gravity is already included..

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