Consider an art crawling along the curve (x - 2) $^{2}$ + y $^{2}$ = 4, where x and y are in meters. the ants starts at the point (4,0) and moves counter - clockwise with a speed of 1.57 meters per second. The time taken by the ant to reach the point (2, 2) is (in seconds)

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Solution

The length of arc of the circle covered by the ant from

(4, 0) to (2, 2) = $\frac{2 π r}{4} = \frac{2 π .2}{4} = π$

So, Distance covered by an Ant. = $π$ mtr

Speed = 1.57 m/sec = $\frac{π}{2}$ m/sec.

So, Time = $\frac{D i s t a n c e}{S p e e d}$ = $\frac{π}{π / 2}$ = 2sec.

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