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The difference in gravitational acceleration depends on the distance from the centre of the earth , not the surface. The equation for the new rate of accelration calculated from the surface rate is:

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a = k / ( ( d / r )2 )

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where:

a = acceleration due to gravity at new position

k = surface rate of acceleration ( use 9.82 (m/s)/s )

d = distance from earths centre to new position ( r + height of jump) ( 6376000 metres)

r = surface radius ( use 6371000 metres )

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Even if you jump from 5,000 metres the rate of acceleration would be :

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9.8046 (m/s)/s , which is 99.84 % of the rate at the surface

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Q: Why does a man get hurt when he jumps from a significant height even though newtons universal gravitational law says that height is inversely proportional to acceleration due to gravity?
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