A television camera is positioned 4000 ft from the base of a rocket launching pad. The angle of elevation of the camera has to change at the correct rate in order to keep the rocket in sight. Also, the mechanism for focusing the camera has to take into account the increasing distance from the camera to the rising rocket. Let's assume the rocket rises vertically and its speed is 900 ft/s when it has risen 3000 ft. (Round your answers to three decimal places.) (a) How fast is the distance from the television camera to the rocket changing at that moment? ft/s (b) If the television camera is always kept aimed at the rocket, how fast is the camera's angle of elevation changing at that same moment? rad/s
A television camera is positioned 4000 ft from the base of a rocket launching pad. The angle of elevation of the camera has to change at the correct rate in order to keep the rocket in sight. Also, the mechanism for focusing the camera has to take into account the increasing distance from the camera to the rising rocket. Let's assume the rocket rises vertically and its speed is 900 ft/s when it has risen 3000 ft. (Round your answers to three decimal places.) (a) How fast is the distance from the television camera to the rocket changing at that moment? ft/s (b) If the television camera is always kept aimed at the rocket, how fast is the camera's angle of elevation changing at that same moment? rad/s
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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Transcribed Image Text:A television camera is positioned 4000 ft from the base of a rocket launching pad. The angle of elevation of the camera has
to change at the correct rate in order to keep the rocket in sight. Also, the mechanism for focusing the camera has to take
into account the increasing distance from the camera to the rising rocket. Let's assume the rocket rises vertically and its
speed is 900 ft/s when it has risen 3000 ft. (Round your answers to three decimal places.)
(a) How fast is the distance from the television camera to the rocket changing at that moment?
ft/s
(b) If the television camera is always kept aimed at the rocket, how fast is the camera's angle of elevation changing
at that same moment?
rad/s
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