How Fast to Launch an Object from Mercury for a Final Speed of 3000 m/s?

AI Thread Summary
To determine the initial speed needed for an object launched from Mercury to achieve a final speed of 3000 m/s, the relevant equation is vi² = vf² + GM/ri. The radius of Mercury is 2440 km, and its mass is 0.3x10^24 kg. A user initially calculated the required speed as 4151.8315 m/s but found this to be incorrect. The discussion highlights the importance of considering the gravitational potential energy in the calculations, indicating that the kinetic energy formula may be missing critical components. Accurate calculations are essential for determining the correct initial launch speed.
ohheytai
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The radius of Mercury (from the center to just above the atmosphere) is 2440 km (2440x10^3 m), and its mass is 0.3x10^24 kg. An object is launched straight up from just above the atmosphere of Mercury.

(a) What initial speed is needed so that when the object is far from Mercury its final speed is 3000 m/s?


Homework Equations


vi² = vf² + GM/ri


The Attempt at a Solution


i got 4151.8315 m/s
and its wrong help me please!
 
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ohheytai said:

Homework Equations


vi² = vf² + GM/ri
The kinetic energy of an object is (1/2)mv2. Do you see what is missing in your formula?

The Attempt at a Solution


i got 4151.8315 m/s
and its wrong help me please!
 

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