Question

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This question is intended to challenge your understanding of sinusoidal models. When the Space Shuttle is fired into orbit from a site such as Cape Canaveral, Florida, which is not on the equator, it goes into an orbit that takes it alternatively north and south of the equator. Its distance from the equator is approximately sinusoidal over time. Suppose the Space Shuttle is fired into orbit from Cape Canaveral and 12 minutes later it reaches its farthest distance north of the equator, 2485 miles. Half a cycle later it reaches its farthest distance south of the equator on the other side of Earth, also 2485 miles. Assume the Space Shuttle completes one orbit every 82 minutes. (a) Sketch one complete cycle of the number of miles, m, the Space Shuttle is from the equator at time t minutes since liftoff. (When the Shuttle is north of the equator consider the distance positive and when it is south of the equator consider the distance negative.) m(t) m(t) 2000 2000 1000 1000 t 20 -1000 -10001 -2000 -2000 O m(t) m(t) 2000 2000 1000 1000 t t -1000) -1000 -2000 -2000

Answer 1