Solved: The position of a particle in the plane at time t

Chapter , Problem 32PE

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The view from Skylab \(4\) What percentage of Earth’s surface area could the astronauts see when Skylab \(4\) was at its apogee height, \(437 km\) above the surface? To find out, model the visible surface as the surface generated by revolving the circular arc \(GT\),shown here, about the \(y-axis\). Then carry out these steps:

Use similar triangles in the figure to show that \(y_{0} / 6380=6380 /(6380+437)\). Solve for \(y_{0}\)..To four significant digits, calculate the visible area as

\(V A=\int_{y 0}^{6380} 2 \pi x \sqrt{1+\left(\frac{d x}{d y}\right)^{2} d y}\)

.To four significant digits, calculate the visible area as

Equation Transcription:

Text Transcription:

4

437 km

GT

y-axis

y_0 /6380 = 6380/(6380 + 437)

y_0

V A = integral_y_0 ^6380 2 pi x sqrt 1 + (dx/dy)^2 dy