Finding impact speed of a high altitude free fall

If we neglect the effects of air resistance, the impact speed of a body of mass m released from rest at an altitude of 2 x 10^8 m above the surface of Earth (mass of earth = M = 5.99 x 10^24 kg, radius of earth = 6.37 x 10^6 m)

It’s a multiple choice and I think I have it, but I just want to make sure because we just scraped over the surface of gravitation.

I used conservation of mechanical energy where ΔU = -GMm/r and ΔK = (1/2)mv^2
Setting them equal and opposite, m cancels and we get:

v^2 = 2GM/r, where r is the radius of earth plus the altitude. I get that the answer is 1968 m/s. Am I doing this correct? I only ask because my answer would then be "None of these is correct" for the multiple choice.

http://ift.tt/1k8ftr9

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