Finding initial speed given final speed

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To determine the initial speed required for an object launched from Mercury to achieve a final speed of 2500 m/s when far from the planet, conservation of energy principles are applied. The radius of Mercury is 2440 km, and its mass is correctly noted as approximately 0.3 x 10^24 kg, correcting earlier misstatements regarding its mass. The discussion highlights the difference in applying conservation of energy for escape speed versus initial speed when the final speed at infinity is above zero. Accurate values are crucial for solving these physics problems. Understanding these principles is essential for calculating speeds in gravitational fields.
jamagner
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The radius of Mercury (from the center to just above the atmosphere) is 2440 km (2440103 m), and its mass is 0.31024 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 2500 m/s?

the second part is about the escape speed which i already figured out
 
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This is another conservation of energy problem.
 
jamagner said:
The radius of Mercury (from the center to just above the atmosphere) is 2440 km (2440103 m), and its mass is 0.31024 kg.

Check your values, by the way. Mercury certainly has more mass than 0.3 kg...

What needs to be different about using conservation of energy to solve for the escape speed versus solving for the starting speed when the speed at infinity is greater than zero?
 
dynamicsolo said:
Check your values, by the way. Mercury certainly has more mass than 0.3 kg...
:smile: A typo, I presume. More like 0.3x10^24 kg.
 

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