- #1
Luke1121
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Homework Statement
Assuming the Earth is at rest and alone in the universe what speed would a spaceship arriving at the surface of Earth from an infinitley large distance be if the speed at infinity= 0 and acceleration is caused only by gravity
Homework Equations
[itex]F= \frac{GmM}{x^2}[/itex]
Also using the chain rule [itex]a=v\frac{dv}{dx}[/itex]
The Attempt at a Solution
well I set ma equal to the force due to gravity so
[itex]v\frac{dv}{dx}= \frac{GM}{x^2}[/itex]
seperating the variables gives [itex]vdv=\frac{GM}{x^2}dx[/itex]
then
[itex]\int vdv=GM\int x^{-2} dx[/itex]
would the limits of integration need to be from infinity to the surface of the earth, or am i on the wrong track all together?