This is not a related rates problem. Also, 1/?5 is about 0.4472 so that is outside the circle. The circle centre (4, 0) with radius 3 is (x - 4)^2 + y^2 = 9 2(x – 4) + 2ydy/dx = 0 dy/dx =-(x – 4)/y = -(x – 4)/?9 – (x – 4)^2 The motion is counterclockwise.
If Alice releases rope when rock is at (2,?5) the rock flies along the tangent to the circle heading near to the origin. Dy/dx = 2/?5 Let y = mx + c be the tangent at that point?5 = 2/?(5)* 2 + c c = 1/?(5) and since this is the y intercept it shows that the rock will meet the y-axis at y = 1/?(5) as Alice wished. N.B. Although not required the tangent will be y = 2/?(5)x + 1/?(5).
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