Cat going home

Calculus Level 2

There is a cat at point $A$ that wants to return home at point $H.$ But the cat must drink water from the river before returning home. What is the minimum distance the cat needs to walk from point $A$ to point $H?$

The answer is 1000.00.

1 solution

Romain Bouchard
Jun 4, 2018

Let's call $x$ the horizontal distance from the cat to the water. Using the Pythagorean Theorem, we can write the distance walked by the cat as $d(x) = \sqrt{300^2+x^2}+\sqrt{300^2+(800-x)^2}$ .

By symmetry we know that distance function hits an extremum for $x=400$ with $d(400) = \sqrt{300^2+400^2}+\sqrt{300^2+(800-400)^2} = 500+500 = 1000$ .

Additionnally, we know that extremum is a minimum because if the cat were to walk straight up to the water and then to his home, it would walk $300+800=1100$ which is longer.

The distance required is the straight-line distance between the cat's reflection in the water, say A', and the point H. This distance or A'H =√[(300+300)²+800²] = 1000 m.

Ajit Athle - 3 years ago

Cat going home

The answer is 1000.00.

1 solution

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