The woman travels in a circle given by the equation x(t) = 20cos(7.5t), y(t) = 20sin(7.5t). Thus the circle's radius is sqrt(x^2 + y^2) = 20 metres.

Take the purse as θ1 = 0°. Then after 18 min, the woman sits at (-14.1, 14.1) by ( x(t),y(t) ); thus θ2...

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The woman travels in a circle given by the equation x(t) = 20cos(7.5t), y(t) = 20sin(7.5t). Thus the circle's radius is sqrt(x^2 + y^2) = 20 metres.

Take the purse as θ1 = 0°. Then after 18 min, the woman sits at (-14.1, 14.1) by ( x(t),y(t) ); thus θ2 = 135°.

The shortest distance to the purse is the chord from θ1 to θ2 (length d). Draw a line from the center to the chord bisecting the angle to form two identical right triangles. Now,

d/2 = 20Sin(135/2) = 18.48 m

**d = 36.96 m**