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

In summary, a rocket with a mass of 1.5 x 10^6 kg is launched from Earth's surface with a speed of 0.5 x 10^4 m/s. Using the basic kinematic equations, the maximum altitude it can reach above the Earth's surface is 6.061 x 10^6 m. However, in order to reach this conclusion, one must take into account the Earth's mass and radius, and equate the kinetic energy of the rocket with its potential energy at a certain height above the Earth's surface. A constant acceleration cannot be assumed in this scenario.
  • #1
Ahmed.Sandman
2
0

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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  • #2
Try equating KE of rocket = PE of rocket above the Earth's surface.
 
  • #3
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 [itex] h [/itex] above its surface.
 

1. What is the maximum altitude a rocket can reach?

The maximum altitude a rocket can reach depends on various factors such as the type of rocket, its design, and the amount of fuel it carries. Typically, rockets can reach altitudes of about 100 kilometers or more.

2. What determines the maximum altitude a rocket can reach?

The maximum altitude a rocket can reach is determined by its initial velocity, acceleration, and the amount of thrust it generates. Other factors such as air resistance and gravity also play a role in determining the maximum altitude.

3. How does the maximum altitude of a rocket affect its performance?

The maximum altitude of a rocket is an important factor in determining its performance. A higher maximum altitude allows the rocket to reach farther distances and carry heavier payloads. It also affects the trajectory and accuracy of the rocket's flight.

4. Can the maximum altitude of a rocket be increased?

Yes, the maximum altitude of a rocket can be increased by improving its design, increasing the amount of fuel or thrust, and reducing air resistance. However, there are limitations to how high a rocket can reach due to the Earth's atmosphere and gravitational pull.

5. What is the record for the highest maximum altitude reached by a rocket?

The record for the highest maximum altitude reached by a rocket is currently held by NASA's Juno spacecraft, which achieved an altitude of 111,846 kilometers above Jupiter's clouds in 2016. The record for a rocket launched from Earth is held by the Saturn V rocket, which reached an altitude of 118 kilometers during the Apollo 17 mission.

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