A single stream of cars, each of width \(a\)
and exactly in line, is passing along a straight road
of breadth \(b\) with speed \(V\). The distance between the
successive cars is \(c\).
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A chicken crosses the road in safety
at a constant speed \(u\) in a straight line making
an angle \(\theta\) with the direction of traffic.
Show that
\[u\geqslant
\frac{Va}{c\sin\theta+a\cos\theta}.\]
Show also that if the chicken chooses \(\theta\) and \(u\)
so that it crosses the road
at the least possible uniform speed, it crosses
in time
\[\frac{b}{V}\left(\frac{c}{a}+\frac{a}{c}\right)
.
\]