A soldier has to cross a 80 m wide river on a ropeway grabbing on a pulley. The length of the rope is 100 m , its ends are fixed at the same height on both banks of the river and the rope is tight at

Question

A soldier has to cross a 80 m wide river on a ropeway grabbing on a pulley. The length of the rope is 100 m , its ends are fixed at the same height on both banks of the river and the rope is tight at shown. The soldier starts from a platform under one of the fixed points with zero initial velocity. (Friction is absent every where.) If the highest speed of the soldier during the crossing is v (in m/s). What is v 2 ?

TestHub · Accepted Answer

Initially (pulley directly under one bank): if the soldier hangs $y$ below bank level, $(100 - y)^{2} = 8 0^{2} + y^{2}$ ⇒ $y = 18$ m.

At the middle (lowest point, hence maximum speed): each rope leg is 50 m across a 40 m half-span: $y^{'} = 5 0^{2} - 4 0^{2} = 30$ m.

Drop $h = 30 - 18 = 12$ m.

$v^{2} = 2 g h = 2 \times 10 \times 12 = 240.00$

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