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Pion's mean free path in a lake. exercIse question
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[QUOTE="tasos, post: 5491150, member: 524875"] [h2]Homework Statement [/h2] 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 [h2]Homework Equations[/h2][h2]The Attempt at a Solution[/h2] 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. [B]BUT [/B]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. [/QUOTE]
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Pion's mean free path in a lake. exercIse question
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