Earth-Asteroid collision problem

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 595 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
V = 2[itex]\pi[/itex]R/T

a = (v^2)/R

3. The attempt at a solution
I am very confused because wouldn’t the speed with which the asteroid hits the earth depend where the asteroid is in relation to the Earth? or does head on imply something I’m missing?

Either way what I thought I should do is calculate the velocity of the Earth around the sun plus the velocity of the asteroid, but that’s not right.

I appreciate your help.


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