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

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SUMMARY

The maximum altitude of a rocket launched from Earth's surface, with a mass of 1.5 x 10^6 kg and an initial speed of 0.5 x 10^4 m/s, is calculated to be 6.061 x 10^6 m. This conclusion is derived by equating the kinetic energy of the rocket at launch with its potential energy at maximum altitude, rather than using constant acceleration kinematic equations. The Earth's mass (5.97 x 10^24 kg) and radius (6.38 x 10^6 m) are critical for accurate calculations, emphasizing the need for gravitational potential energy considerations.

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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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