Calculating Impact Speed of Asteroid on Earth - Neglecting Atmospheric Friction

[ninjagowoowoo]

Q:
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 4.85×10^9 kg. It is approaching the Earth on a head-on course with a velocity of 593 m/s relative to the Earth and is now 4.85×10^6 km away. With what speed will it hit the Earth's surface, neglecting friction with the atmosphere?

I found g using (mass of earth)(mass of sat)/(r^2)
of course since x = 4.85×10^6 km = 4.85×10^9 m
so g=
(5.98e24)/(4.85e9) <--since one of the r's cancels out with the mass of sat
then i used v^2 = vo^2 + 2ax
using g as a and everything else is pretty explanitory.

Where'd I go wrong?

 

[ninjagowoowoo]

.. i forgot the G in the equation... but yeah it's still wrong..

 

[siddharth]

You can use the equation v^2=u^2+2as, if "a" is constant. When we usually use this formula (ex: projectile motion),we assume the value of g to be fairly constant.

In this case, the gravitational force is not constant, and is varying with distance. So you cannot use the formula v^2=u^2 + 2as.

Ill give you a hint. There is another way (a much easier one) you should approach the problem with. What do you usually use when you want to find final velocities?
(Example, an object is dropped at a height h.What is its velocity when it reaches the ground?)