Answered: To prepare astronauts for the…

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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Question

To prepare astronauts for the experience of zero gravity (technically, microgravity) in space, NASA uses a specially designed jet. A pilot accelerates the plane upward to an altitude of approximately 9,000 meters and then reduces power. During the time of reduced power, the plane is in freefall and the astronauts experience microgravity. The altitude

A(t),

in meters, of the plane t seconds after power was reduced can be approximated by

A(t) = −4.9t² + 90t + 9,000.

The graph is shown as follows.

A coordinate plane is given with a plane flying along a curve. The horizontal axis is labeled "Time (seconds)". The vertical axis is labeled "Altitude (meters)". The curve starts at approximately (−5, 8400), goes up and right becoming less steep, passes through (0, 9000) labeled "Microgravity begins here," changes direction at approximately (9, 9400), goes down and right becoming more steep, passes through approximately (18, 9000) labeled "Microgravity ends here," and exits the right side of the window.

If the pilot increases power when the plane descends to 9,000 meters, ending microgravity, find the time (in seconds) the astronauts experience microgravity during one of these maneuvers. Round to the nearest tenth of a second.

sec

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