The Brainliest Answer!

This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Earth's radius = R miles, Mass of earth = M kg, mass body = m kg

Energy of the body at height 500mi = 800 km when projected:  P.E. + K.E. = - \frac{GMm}{(R+800)} + \frac{1}{2} m v1^2

Suppose it goes away from Earth and revolves in an Orbit around the Earth at radius X > R, then

Energy of the body at height X :  P.E. + K.E. = - \frac{GMm}{(R+X)} + \frac{1}{2} m v2^2. \\ \\ Let us say the body has very near zero velocity as it nears infinite distance away from Earth.  If the body nears infinite distance, then its energy will be  zero as R+X ⇒ Infinity.

So, Energy of the body at height 500mi to go to infinity  = 0 = - \fracGMm}{R+800} + \frac{1}{2} m v1^2 \\ v1 = \sqrt{\frac {2GM}{R+800}} \\ \\ = \sqrt{\frac{2*6.67*10^{-11}*6*10^{24}}{7170*10^3}} = 10.565 km/sec

2 3 2