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Calculus Pup

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aweld98

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 I just returned from a calc group session at school with my friends and our calculus teacher.  My friend, in an attempt to make Taylor Polynomials and series less of a burden, brought along her little dog.  Ironically, as I was sitting there, the pup inspired what I am afraid will be my final blog post of my AP Physics C year.  Well, my friend had gotten up from her seat, and the dog, which was tied by a leash to the chair, wanted a change of scenery.  As a result, she attempted to jump onto the very chair which she was tied onto.  However, as soon as her paws came in contact with the chair, she skid across the surface of the chair and nearly fell off the opposite side.  So, what did the little doggy fail to consider in her take off towards the chair?  Well, there are a few factors.  First off, when the dog took off from her hind legs, she made an angle with the floor; she had both horizontal and vertical components to her velocity.  As a result, when she hit the peak of her trajectory path, hence landing on the chair, her vertical velocity was zero, but her body continued to move in the horizontal direction due to the horizontal component of her velocity.  In addition, because the surface of the chair is slicker than most surfaces, resulting in a lower coefficient of friction, there was little frictional net force present in order to decelerate her horizontal velocity.  Ideally, in order to prevent any skidding, the dog would simply have jumped completely vertical and landed on the chair, hence having zero horizontal velocity (this application is not ideal, however, because it would involve the dog jumping through the solid seat of the chair, which is impossible and would hurt, to say the least).  However, a large angle with the horizontal would increase the sine component of her velocity and minimize her horizontal velocity, and therefore skidding.

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