Riding With a Particle: Measuring Its Lifetime

[cshelbythec]

A particle lives for a short time before breaking apart into other particles. Suppose it is moving at a speed of 0.996c, and an observer who is stationary in a laboratory measures the particle's lifetime to be 3.00 10-8 s.
What is the lifetime according to a hypothetical person who is riding along with the particle?

The Attempt at a Solution

I tried
t=t(0)/(1-v2/c2)^1/2
where t=3.00 10-8s and I'm finding t(0) proper.
my answer is 3 10-9 which is wrong. what am I doing wrong?

 

[rootX]

A particle lives for a short time before breaking apart into other particles. Suppose it is moving at a speed of 0.996c, and an observer who is stationary in a laboratory measures the particle's lifetime to be 3.00 10-8 s.
What is the lifetime according to a hypothetical person who is riding along with the particle?

The Attempt at a Solution

I tried
t=t(0)/(1-v2/c2)^1/2
where t=3.00 10-8s and I'm finding t(0) proper.
my answer is 3 10-9 which is wrong. what am I doing wrong?

i have forgotten this stuff, but try multiplying it if dividing doesn't work

 

[Doc Al]

my answer is 3 10-9 which is wrong. what am I doing wrong?

I suggest carrying more significant figures in your answer.