Projectile Motion: Finding Maximum Height with Mechanics and Gravitation

[zorro]

Homework Statement

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

Homework Equations

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

I don't understand which approach is correct. Please help!

 

[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..

 

[The legend]

your welcome