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Two rail tracks ,which make an angle $X$ with each other ,intersect at $O$. Two trains $P$ and $Q$ are travelling on these tracks with speeds $u$ and $v$ towards $O$. Initially $P$ & $Q$ are at distance $a$ & $b$ from $O$ respectively. Show that the shortest distance between the train is

$\frac{(av - bu)\sin X}{(u^2+v^2-2uv \cos X)}$

And show that trains would collide if

$\frac{u}{v} = \frac{a}{b}$

A clear explanation would be great.

Sandeep Thilakan
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On the way to success
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1 Answers1

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Hint: Shortest distance = $\sqrt{a^2 + b^2 - 2\cdot a\cdot b\cdot cos(x)}$

abstractnature
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  • Can u describe it further ? – On the way to success Feb 14 '14 at 10:18
  • I can describe it, but what you have to prove is not the shortest distance actually, it is the rate of change of that shortest distance, which you can immediately see by differentiating this equation. So your question is not much clear, that whether you are asking shortest distance, or instantaneous rate of change of that distance. – abstractnature Feb 14 '14 at 10:22