Fonder Woman and Superman fly to an altitude of 1650 km, carrying between them a

Question

Fonder Woman and Superman fly to an altitude of 1650 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 inaccessible to their evil enemies who are trying to gain possession of it, yet keep 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 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 10^24 kg, respectively.

Explanation / Answer

Since , the altitude of 1650 km is significantly large and thus the value of acceleration due to gravity doesnot remain constant. we know that the value of gravity decreases as altitude increase and it is maximum at the surface of the earth (i.e. 9.8 m/sec2).

Nevertheless, let us assume the gravity value is same in this case. then, by appying the Newton law of motion :

u=0, v= to find out , a=g= 9.8, s=height= 1650000 m

then,

v2 = 2*9.8*1650000

v= 5686 m/s

The answer given with the question is nearly half of the calculated one. I am sure of mine if I consider gravity as constant parameter.

Note: The gravity value at height of 1650 km is about 6.1 m/sec2.

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