M1 v1 = (m1 + m2)v2.
All of the exponents should be lowered to the bottom right of the letters.
Answer:
v = √2G
/ R
Explanation:
For this problem we use energy conservation, the energy initiated is potential and kinetic and the final energy is only potential (infinite r)
Eo = K + U = ½ m1 v² - G m1 m2 / r1
Ef = - G m1 m2 / r2
When the body is at a distance R> Re, for the furthest point (r2) let's call it Rinf
Eo = Ef
½ m1v² - G m1
/ R = - G m1
/ R
v² = 2G
(1 / R - 1 / Rinf)
If we do Rinf = infinity 1 / Rinf = 0
v = √2G
/ R
Ef = = - G m1 m2 / R
The mechanical energy is conserved
Em = -G m1
/ R
Em = - G m1
/ R
R = int ⇒ Em = 0
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This is my opinion so don't really take my word for it, but we as humans are an evolved species of mammals. So we are a lot more complex in our structure than most animals or insects, but then again through history we made lots of discoveries because we created new technology or out of pure curiosity tried new thing like building better civilizations, even though ours today is destroying the earth but besides the point, and new materials that we can use and all that. So we have made mistakes but that doesn't always mean we are a mistake as a whole