Four rods each of length l have been hinged to form a rhombus. Vertex A is fixed to rigid support, vertex C is being moved along the x -axis with constant velocity v as shown in the figure. The rate a

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Four rods each of length l have been hinged to form a rhombus. Vertex A is fixed to rigid support, vertex C is being moved along the x -axis with constant velocity v as shown in the figure. The rate at which vertex B is approaching the x -axis at the moment the rhombus is in the form of a square is

TestHub · Accepted Answer

In the figure, draw a perpendicular BE from B to line AC , according to Pythagoras theorem BE 2 + AE 2 = l 2 or y 2 + x 2 2 = l 2 ∴ 2 y dy dt + x 2 ⋅ dx dt = 0 ⇒ - dy dt = 1 2 x 2 y ⋅ dx dt x = 2 y , As the rhombus is in the form of a square. Hence, v B = l 2 v c = v 2

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