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1. An earth satellite has an apogee of 40,000 km and a perigee of 6,600 km. Assuming the radius of the earth as 6,400 km, what will be the eccentricity of the elliptical path described by the satellite with the center of the earth at one of the foci?

1. An earth satellite has an apogee of 40,000 km and a perigee of 6,600 km. Assuming the radius of the earth as 6,400 km, what will be the eccentricity of the elliptical path described by the satellite with the center of the earth at one of the foci?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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EXERCISES: 1. An earth satellite has an apogee of 40,000 km and a perigee of 6,600 km. Assuming the radius of the earth as 6,400 km, what will be the eccentricity of the elliptical path described by the satellite with the center of the earth at one of the foci? 2. A tunnel through a mountain for a four lane highway is to have a elliptical opening. The total width of the highway (not the opening) is to be 16 m, and the height at the edge of the road must be sufficient for a truck 4 m high to clear if the highest point of the opening is to be 5 m approximately. How wide must be the opening be? 3. At a water fountain, water attains a maximum height of 4 m at a horizontal distance of 0.5 m from its origin. If the path of water is a parabola, find the height of water at a horizontal distance of 0.75 m from the point of origin? 4. Cross section of a Nuclear cooling tower is in the shape of a hyperbola with equation 30² 44² The tower is 150 m tall and the distance from the top of the tower to the center of the hyperbola is half the distance from the base of the tower to the center of the hyperbola. Find the diameter to the top and base of the tower. 150m
Transcribed Image Text:EXERCISES: 1. An earth satellite has an apogee of 40,000 km and a perigee of 6,600 km. Assuming the radius of the earth as 6,400 km, what will be the eccentricity of the elliptical path described by the satellite with the center of the earth at one of the foci? 2. A tunnel through a mountain for a four lane highway is to have a elliptical opening. The total width of the highway (not the opening) is to be 16 m, and the height at the edge of the road must be sufficient for a truck 4 m high to clear if the highest point of the opening is to be 5 m approximately. How wide must be the opening be? 3. At a water fountain, water attains a maximum height of 4 m at a horizontal distance of 0.5 m from its origin. If the path of water is a parabola, find the height of water at a horizontal distance of 0.75 m from the point of origin? 4. Cross section of a Nuclear cooling tower is in the shape of a hyperbola with equation 30² 44² The tower is 150 m tall and the distance from the top of the tower to the center of the hyperbola is half the distance from the base of the tower to the center of the hyperbola. Find the diameter to the top and base of the tower. 150m
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