April 03, 2014

§10.2 - The Parabola

Word Problems

1. A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strike the surface of the dish and are reflected to a single point, where the receiver is located. If the dish is 10 feet across at its opening and is 3 feet deep at its center, at what position should the receiver be placed?

April 03, 2014

2. A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 24 inches across at its opening and is 2 feet deep, where will the light be concentrated?

3. A search light is shaped like a paraboloid of revolution. If the light source is located 3 feet from the base along the axis of symmetry and the opening is 8 feet across, how deep should the searchlight be?

April 03, 2014

4. A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 138 feet and a maximum height of 40 feet. Find the height of the arch at 5 feet from its center.

5. A reflecting telescope has a mirror shaped like a paraboloid of revolution. If the distance of the vertex to the focus is 25 feet and the distance across the top of the mirror is 72 inches, how deep is the mirror in the center?

WARM-UP! (on the sheet from yesterday)

April 03, 2014

6. An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers are both 4 inches tall and stand 40 inches apart. Find the vertical distance from the roadway to the cable at a point on the road 8 inches from the lowest point of the cable.

7. An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers stand 30 inches apart. At a point between the towers and 10 inches along the road from the base of one tower, the cable is 1 inches above the roadway. Find the height of the towers.

April 03, 2014

8. A spotlight has a parabolic cross section that is 6 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus? Round answer to two decimal places.