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## Homework Statement

Charged pion with average life time $$\tau=10^{-8} sec$$, and mean free path in the water$$\ell=100m$$ falls prependicular to a lake (depth of lake is at $$\ell_0 =30m$$ with velocity $$V=0.9999c$$

What of the next is correct?

1). The particle isn't gona touch the bottom of the lake

2.)The particle have at least 60% probability to touch the lake

3.)The particle have a probability lower than 40% to touch the bottom of the lake

## Homework Equations

## The Attempt at a Solution

The first think i did is to calculate the Height of the lake "seen" by the pion

$$L=\ell_ 0 \sqrt{1+\frac{V^2}{c^2} } =0.42m$$

After that i calculate the time needs to touch the bottom of the lake

$$t=\frac{L}{V} =0.14 \times 10^{-8} $$

So if pion's life time is $$\tau=10^-8 sec$$ and it needs $$t=0.14 \times 10^{-8} $$, i say that it not gona touch the bottom of the lake.

**BUT**the excersice is giving me also the mean free path in the water$$\ell=100m$$

and i don't know how to use it, or if i need to use it.

Any sugestions? Thanx a lot.