Time dilation question (2 Viewers)

[elfanger]

Help me with this question please:

"Mesons have a life of 2.2 micro seconds. however, mesons formed in the upper atmosphere as air particles are hit by cosmic rays take 16 micro seconds to reach the ground. calculate the speed of the meson."

Thanks.

 

[BlackJack]

The best thing to use is time dilation; this is what the question wants you to do.

btw, assume that the meson dies upon reaching the ground and so have a life of 16 microseconds.
That is, you know t and t[0] from this equation.
t = t[0] / sqrt ( 1 - v^2/c^2 )

 

[lil princess]

I hope you can follow this...

rearrange above eqn [BlackJack];

t = t[o] / sqrt ( 1 - v^2/c^2 )

sqrt ( 1 - v^2/c^2) = t[o] / t

1 - v^2/c^2 = t[o]^2/t^2

v^2/c^2 = 1 - t[o]^2/c^2

v^2 = c^2 ( 1 - t[o]^2/t^2 )

therefore;

v = (c) sqrt ( 1 - t[o]^2/t^2)

substitue given values into eqn and speed of light and will give you answer.