Meteor Tracking 2: A meteor originally moving along a straight path will be deflected by

Chapter 12, Problem 6

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Meteor Tracking 2: A meteor originally moving along a straight path will be deflected by Earths gravity into a path that is a conic section. If the meteor is moving fast enough, the path will be a hyperbola with the original straight-line path as an asymptote. Assume that a meteor is approaching the vicinity of Earth along a hyperbola with general equations x = a sec t y = b tan t a. Suppose that at t = 1.4, the position of the meteor is (x, y) = (29.418, 11.596), where x and y are displacements in millions of miles. Find the particular values of a and b. b. Plot the branch of the hyperbola in the range for t of . Sketch the result. c. Earth is at the focus of the hyperbola that is closest to the vertex in part b. What is the focal radius? How far is the meteor from Earth when it is at the vertex of the hyperbola? d. Assuming that the meteor does not hit Earth, its path as it leaves Earths vicinity will approach the other asymptote of the hyperbola. What is the equation of this other asymptote? Show both asymptotes on your sketch in part b.