(a) The span of the parabolic arch in Figure B is 8 m. At a distance of 2 m from the

Chapter 11, Problem 41

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(a) The span of the parabolic arch in Figure B is 8 m. At a distance of 2 m from the center, the vertical clearance is 4.5 m. Find the height of the arch. Hint: Choose a convenient coordinate system in which the equation of the parabola will have the form x2 4p(y k). Figure B (b) Figure C shows the same parabolic arch as in Figure B. Suppose that from a point P on the base of the arch, a laser beam is projected vertically upward. As indicated in the figure, the beam hits the arch at a point Q and is then reflected. Let R denote the point where the beam crosses the axis of the parabola. How far is it from R to the base of the arch? (That is, what is the perpendicular distance from R to the base?) F