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Calculus Level 5

A dog sees a rabbit running in a straight line across an open field and gives chase. In a rectangular coordinate system (as shown in the figure), assume:

(i) The rabbit is at the origin and the dog is at the point (L,0)(L,0) at the instant the dog first sees the rabbit.

(ii) The rabbit runs up the yy-axis and the dog always runs straight for the rabbit.

(iii) The dog runs at twice the speed of the rabbit.

Assuming L=300L=300 units, how much does the dog have to travel to catch the rabbit?

Enter your answer as the distance the dog has traveled from sight to meal.


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