So far this has really got me stumped, I have tried several different solutions,

Question

So far this has really got me stumped, I have tried several different solutions, so please take your time on this one, and make your solution step by step so I dont get lost. Thanks.

Wonder Woman and Superman fly to an altitude of 1610 km, carrying between them a chest full of jewels that they intend to put into orbit around Earth. They accidently drop the chest, which leaves their weary hands at rest, and discover that they are no longer capable of catching it as it falls into the Pacific Ocean. At what speed does the chest impact the surface of the water? Ignore air resistance, although in the real world it would make a world of difference. The radius and mass of Earth are 6370 km and 5.98

So far this has really got me stumped, I have tried several different solutions, so please take your time on this one, and make your solution step by step so I dont get lost. Thanks. Wonder Woman and Superman fly to an altitude of 1610 km, carrying between them a chest full of jewels that they intend to put into orbit around Earth. They accidently drop the chest, which leaves their weary hands at rest, and discover that they are no longer capable of catching it as it falls into the Pacific Ocean. At what speed does the chest impact the surface of the water? Ignore air resistance, although in the real world it would make a world of difference. The radius and mass of Earth are 6370 km and 5.98 times 1024 kg, respectively. Incorrect. You appear to have assumed that the acceleration due to gravity is the same at all altitudes and equals its value at Earth's surface. Answers Found Wrong: 5617.47 m/s , 5651.87 m/s , 5608.93 m/s , 5626.03 m/s , 5634.60 m/s

Explanation / Answer

balancing the energy ,

-GM /(R+h) = -GM/R + 1/2 v^2

GM ( 1/ R- 1/(R+h) = 1/2 v^2 ,
so ,
putting values

6.67*10^-11 * ( 5.98*10^24) ( 1/6370000 -1/(6370000+1610000) ) = 1/2 v^2

solving it ,

v = 5026.55 m/s = 5.0266 km/s

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