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zorro
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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!