A 1.0 object is released from rest 500Km above the earth. 1. What would the impa

Question

A 1.0 object is released from rest 500Km above the earth. 1. What would the impact speed be if the earth were flat? 2. By what percentage is the flat-earth calculation in error?

Explanation / Answer

If earth is flat: (1/2)mv^2 = mgh --->v= sqrt(2gh) = sqrt(2*9.81*500*10^3) = 3132 m/s If earth is round the gravitational field strength g=GM/r^2 is not constant, hence we must make us of the universal law of gravity to calculate the potential energy GM/r^2 = (1/2)mv^2 --> ((6.67*10^-11)*(5.97*10^24*10^3))/((500*10^3)^2)= (1/2)v^2 --> v= 1784 m/s percentage error = (3132-1784)/1784 = 75.5%

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