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Math Help - Relativety Question

  1. #1
    Mtl
    Mtl is offline
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    Relativety Question

    if a particle is moving with a speed v with respect to Earth, for what value of v/c will the lifetime of the particle be increasesd by 10% above its lifetime when at rest?

    (i know its not entirely a math question... bu i cant figure out the math involved)
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  2. #2
    Senior Member JaneBennet's Avatar
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    If the lifetime of the particle at rest is t, its lifetime when moving at speed v will be \frac{t}{\sqrt{1-\frac{v^2}{c^2}}}.

    So you need to solve the equation

    \color{white}.\quad. \frac{t}{\sqrt{1-\frac{v^2}{c^2}}}\ =\ \left(1+\frac{1}{10}\right)t

    That should give \frac{v}{c}=\frac{\sqrt{21}}{11}\approx41.66\%.
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