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## Homework Statement

An astronaut went to sun from earth by a rocket. According to the clock in the rocket, the traveling time was 5 minute. What was the velocity of the rocket?

( earth is 8 light minute away from sun)

## Homework Equations

[itex]t = \frac {t_0}{\sqrt {1 - \frac{v^2}{c^2}}}[/itex]

## The Attempt at a Solution

According to the reference frame of earth, the distance between sun and earth is, [itex]L_0 = 8\cdot 60 \cdot c [/itex]

Let, the time required to travel this distance be [itex]t_0[/itex] [according to earth];

So, [itex]t_0 = 5 \cdot 60 \cdot \sqrt {1 - \frac{v^2}{c^2}}[/itex]

and the velocity, [itex] v = \frac {L_0}{t_0} = \frac { 8\cdot 60 \cdot c }{ 5 \cdot 60 \cdot \sqrt {1 - \frac{v^2}{c^2}}} = \frac { 8c }{ 5 \sqrt {1 - \frac{v^2}{c^2}}} [/itex]

[itex]v^2 = \frac {64c^2}{25(1 - \frac{v^2}{c^2})}[/itex]

[itex]v^2 \cdot 25(1 - \frac{v^2}{c^2}) = 64c^2[/itex]

Simplifying, [itex]\frac{25}{c^2} (v^2)^2 - 25 (v^2) +64c^2 = 0 [/itex]

**But, the solution of this equation is complex number.**