(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A NASA satellite has just observed an asteroid that is on a collision course with the Earth. The asteroid has an estimated mass, based on its size, of 5 × 10^9 kg. It is approaching the Earth on a head-on course with a velocity of 611 m/s relative to the Earth and is now 5.0 × 10^6 km away. With what speed will it hit the Earth's surface, neglecting friction with the atmosphere?

2. Relevant equations

.5(m*v1^2) + mgh = .5(m*v2^2) + mgh

Fg =G(m*me/re^2) where me = mass of earth and re = radius of earth or in this case distance of the object. I believe the standard excepted value for mass of the earth is 5.89*10^24 kg. *edit* and the excepted value for G = 6.67*10^-11 *edit*

3. The attempt at a solution

First off I've converted the distance into meters.

The approach I've been trying is to find the kinetic energy at a speed of 611 m/s (incredibly easy) and find the potential energy at a distance of 5*10^9 m away. Then add them together and solve for v2 in the first equation. Unfortunately the gravitational pull at this distance is not 9.8 m/s. Because of this I've been trying to use the second equation to determine the gravitational pull at that distance and then substitute it into the first equation as g. But try as I might I can not get the right freaking answer. Any help would be greatly appreciated.

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# Final velocity of an asteroid

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