Distance Travelled by a Particle with Lifetime of 1*10^8 sec

[asdf1]

for this question:
a certain particle has a lifetime of 1*10^8 sec when measured at rest. How far does it go before decaying if its speed is 0.99c when it is created?

my problem:
because the particle is decaying, then its speed should be changing...
then there's two variables in this problem!
any suggestions?

 

[Physics Monkey]

The particle doesn't change its speed until it decays, why would it? This is a standard time dilation problem I think.

 

[Astronuc]

my problem:
because the particle is decaying, then its speed should be changing...

This is not correct. The decay is essentially instantaneous.

One must think of the relativistic effects on time and distance - time dilation and length contraction.

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html

 

[Doc Al]

Don't worry about its speed after decaying. According to lab frame observers, what's the lifetime of the particle? (Hint: Time dilation.)

 

[Physics Monkey]

Well we jumped all over this one. Haha.

 

[Doc Al]

At least we're all saying the same thing. That's good.

 

[asdf1]

opps! lol...

 

[jinksys]

I thought I'd piggy back on this post since I have essentially the same question.

A particle has a lifetime of 1.0E-7s when measured at rest. What distance does it travel if it is created at 0.99c?

I use the time dilation equation to find t'. I get 1.41E-8s. I then multiply this by 0.99c and get 4.19m. The book says 210m.

edit:
Got it

My book's wording gets the best of me, when it says 'at rest' it means the observer, not the particle itself.