A probe to sun - 3

Classical Mechanics Level 3

A payload is fired from Earth's surface with initial speed $v_0 = 2\times 10^4$ m/s. If the mass and radius of earth are $M = 6\times 10^{24}$ Kg and $R = 6.4\times 10^6$ m, find the payload's speed when it is very far from the Earth (in m/s).

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The answer is 16581.2.

1 solution

Rishabh Deep Singh
Feb 9, 2016

$Using\quad energy\quad conservation\\ { U }_{ i }{ +K.E. }_{ i }{ =U }_{ f }{ +K.E. }_{ f }\\ -\frac { G{ M }_{ earth }{ M }_{ load } }{ { R }^{ 2 } } +\frac { { M }_{ load }{ \left( u \right) }^{ 2 } }{ 2 } =0+\frac { { M }_{ load }{ \left( V \right) }^{ 2 } }{ 2 } \\ as\quad potential\quad engergy\quad U\quad at\quad very\quad far\quad way\quad is\quad 0\\ V=\sqrt { \left[ { \left( u \right) }^{ 2 }-\frac { G{ M }_{ earth } }{ { R }^{ 2 } } \right] }$

A probe to sun - 3

if you are lost see this

The answer is 16581.2.

1 solution

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