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Tuesday, 24 October 2017

5 Problems relating in Conic Sections(Pre-calculus)

1. A two-lane highway goes through a semicircular tunnel that is 14 feet high at the top. If each lane is 12 feet wide, how high is the tunnel at the edge of each lane?

2. An arch for a bridge over a highway is in the form of a half ellipse. The top of the arch is 20 feet above the ground level. The highway has four lanes, each 12 feet wide; a center safety strip 8 feet wide; and two side strips, each 4 feet wide. What should the span of the bridge be if the height 28 feet from the center is to be 13 feet?

3. The outer door of an airplane hangar is in the shape of an ellipse. The door is 120 feet across and 90 feet high. Find an equation describing the door’s shape. If you are 6 feet tall, how far must you stand from the edge of the door to keep from hitting your head?

4. An engineer designs a satellite dish with a parabolic cross section. The dish is 15 feet at the opening and the depth is 4 feet. Find the position if the light source (the focus). How far is it from the deepest part of the dish

5. A search light is shaped like a parabolic revolution. If the light source is located 2 feet from the base along the axis symmetry and the depth of searchlight is 4 feet, what should the width of the opening be?
























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