Finding initial speed given final speed

[jamagner]

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

 

[Doc Al]

This is another conservation of energy problem.

 

[dynamicsolo]

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?

 

[Doc Al]

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

A typo, I presume. More like 0.3x10^24 kg.