Maths question about variation

[匿名]

2013-05-02 8:02 am

Weight on and above the earth's surface varies inversely as the square of the distance from the earth's centre; on and below the surface it varies as the distance from the centre. The earth's radius being taken as 6500 km, at what distance below the surface of the earth is the weight on an object the same as at 81.5 km above it?

回答 (1)

不用客氣

2013-05-02 9:26 am

✔ 最佳答案

W : weight
d (km) : distance from the earth's centre

On and above the earth's surface :
W ∝ 1/d²
Hence, W = k1/d²
where k1 is a constant.

On and below the earth's surface :
W ∝ d
W = k2d
where k2 is a constant.

On the earth's surface (d = 6500) :
k1/6500² = K26500
Hence, k1 = 6500³k2

When an object is 81.5 km above the earth's surface :
k1/(6500 + 81.5)² = k2d
6500³k2/6581.5² = k2d
d = 6500³/6581.5²
d = 6340

Distance below the earth's surface
= (6500 - 6340) km
= 160 km

參考: 不用客氣

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