Max Height of Rocket A Above Earth's Surface

AI Thread Summary
To calculate the maximum height H of a rocket launched from Earth's surface, the conservation of energy principle is applied. The initial kinetic energy of the rocket is given by (1/2)mv0^2, while the gravitational potential energy must account for the varying gravitational force at different distances from the Earth's center. The correct formula to use is (1/2)mv0^2 - (GMm)/Re = -(GMm)/(H+Re), which incorporates the distance from the Earth's center. The user initially misapplied the potential energy terms, leading to an incorrect height calculation. The correct maximum height is determined to be 4.08 x 10^6 meters.
eurekameh
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A rocket of mass m=1.20x10^3 kg is launched vertically upward from the Earth's surface with an initial speed v0 = 7.00 km/s.
Calculate the maximum height H of point A above the Earth's surface at which the rocket will momentarily come to rest, before it starts falling back on the earth.

So I know energy (kinetic and potential) is conserved? I've tried using E(initial) = E(final) --> (1/2)mv0^2 = mgh, but figured this wouldn't work because g is not 9.8 m/s^2 far from the earth. Instead, I used (1/2)mv0^2 - (GMm)/Re = -(GMm)/H. I solved for H, but it did not give me the correct solution, which is 4.08 x 10^6. Can anyone help me out?
 
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Check your use of distance in the potential energy terms.
 
Filip Larsen said:
Check your use of distance in the potential energy terms.

I'm supposed to use (1/2)mv0^2 - (GMm)/Re = -(GMm)/(H+Re), aren't I? Lol. Thanks!
 

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