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arpon
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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.