What is the maximum altitude of a rocket launched from Earth's surface?

AI Thread Summary
The discussion focuses on calculating the maximum altitude a rocket can reach when launched from Earth's surface with a given mass and initial speed. The correct approach involves equating the kinetic energy of the rocket at launch with its gravitational potential energy at maximum altitude, rather than using basic kinematic equations. It is emphasized that the Earth's radius and mass should be considered in the calculations to determine the potential energy accurately. The provided solution indicates a maximum altitude of approximately 6.061 x 10^6 m. Understanding the relationship between kinetic and potential energy is crucial for solving this problem.
Ahmed.Sandman
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Homework Statement



A rocket of mass 1.5 x 10^6 kg is launched upward from the surface of the Earth (mass ME = 5.97 x 10^24 kg, radius RE = 6.38 x 10^6 m) with a speed of 0.5 x 10^4 m/s. The rocket will reach a maximum altitude above the surface of the Earth of


Homework Equations


I thought I can solve it with the basic kinematic equations
v^2=v0^2+2*a*delta(x)

The Attempt at a Solution


the right answer is 6.061*10^6m (according to the online quiz)
but I can't reach that conclusion using the equation

I'm not using the Earth's radius or mass

enlighten me please
 
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Try equating KE of rocket = PE of rocket above the Earth's surface.
 
You cannot assume a constant acceleration here. Equate the kinetic energy of the rocket at the surface of the Earth with it's potential energy at a height h above its surface.
 
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