Question

A rocket is launched straight up from the earth's surface at a speed of 14500 m/s. What is its speed when it is very far away from the earth?

Answer #1

We know that energy is conserved .

Now total energy at the surface of the earth = total energywhen it is far away from earth.

total energy at the surface of the earth
=(1/2)mu^{2}- GMm/R

total energy when it is far away from earth
=(1/2)mv^{2}

Then
(1/2)mu^{2}- GMm/R
=(1/2)mv^{2}

(1/2)u^{2}
- GM/R =(1/2)v^{2}

v
= ?[ u^{2} - (2GM/R)] ---------1

Here G = 6.67 *10^{-11}Nm^{2}/kg^{2}

M = mass ofthe
earth = 5.98 *10^{24}kg

R =radius of the earth = 6400 km = 6400000 m

u = speed ofthe rocket at the surface of the earth = 1.45

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