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A ballet dancer doing a grand jete (great leap; see Fig) seems to float horizontally in the central portion of her leap. Show how the dancer can maneuver her legs in flight so that, although her center of mass does indeed follow the expected parabolic trajectory, the top of her head moves more or less horizontally. (See "The Physics of Dance," by Kenneth Laws, Physics Today, February 1985, p. 24.)

A ballet dancer doing a grand jete (great leap; see Fig) seems to float horizontally in the central portion of her leap. Show how the dancer can maneuver her legs in flight so that, although her center of mass does indeed follow the expected parabolic trajectory, the top of her head moves more or less horizontally. (See "The Physics of Dance," by Kenneth Laws, Physics Today, February 1985, p. 24.)

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
8 years ago
When the ballet dance does a great leap, she stretches her legs such that the legs become parallel to the ground. This shifts the center of mass closer to her head from where it was when she was standing on the ground. As the dancer return back to the ground, she brings the center of mass back to the original position by lowering her legs.
Therefore one can see that during the leap, the distance between the center of mass of the ballet dancer and her head increases first, remains fixed for some time and then increased again. When the ballet reaches near the maximum height of flight, her head moves almost horizontal to the changing position of center of mass. Thus, for this very short time, the observer perceives the parabolic motion of center of mass, but the horizontal motion of her head.

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