Question: A small weight is dragged across a horizontal plane by a string PQ of length a, the end P being attached to the weight while

A small weight is dragged across a horizontal plane by a string PQ of length a, the end P being attached to the weight while the end Q is made to move steadily along a fixed line perpendicular to the original position of PQ. Choosing the coordinate axes so that Oy is that fixed line and Ox passes through the initial position of P, as shown in Figure 8.14, show that the curve y = y(x) described by P is such that

dy dx V(a - x) X

The resulting curve is called a tractrix.

P O Figure 8.14 a X

dy dx V(a - x) X

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