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Locoism
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Homework Statement
Suppose a rocket is launched from the surface of the Earth with initial velocity
[itex] v_0 = \sqrt(2gR) [/itex], the escape velocity.
a) Find an expression for the velocity in terms of the distance x from the surface of the Earth (ignore air resistance)
b) Find the time required for the rocket to go 240,000 miles. Assume R = 4000 miles, and g = 78,545 miles/h2
The Attempt at a Solution
So I figure we use [itex] \frac{dv}{dt} = -\frac{mG}{(R+x)^2} [/itex] and multiply by [itex]\frac{dt}{dx} = \frac{1}{v}[/itex] to get
[itex] \frac{dt}{dx} \frac{dv}{dt} = \frac{dv}{dx} = -\frac{mG}{v (R+x)^2} [/itex]
which gives [itex] v(x) = \sqrt(\frac{2mG}{R+x}) + C [/itex]
Using [itex] v(0) = \sqrt(2gR) [/itex] gives
[itex] C = \sqrt(2gR) - \sqrt(\frac{2mG}{R}) [/itex]
I don't know where to go from here...