Wonder Woman and Superman fly to an altitude of 1570 km, carrying between them a

Question

Wonder Woman and Superman fly to an altitude of 1570 km, carrying between them a chest full of jewels that they intend to put into orbit around Earth. They want to make this tempting treasure inaccessable to their evil enemies who are trying to gain possession of it, yet keept it available for themselves for future use when they retire and settle down. But perhaps the time to retire is now! They accidently drop the chest, which leaves their weary hands at rest, and sicover 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*10^24 kg, respectively.

Explanation / Answer

The loss in potential energy equals gain in kinetic energy:

GMm(1/6370000 m - 1/7880000 m) =

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