Explanation Given information: Rate = 20 ft per minute Distance between TV camera and building = 600 ft Calculation: According to the question, Let θ be the angle of elevation. If y(t) is the length of the ball, then tan θ = y ( t ) 600 y ( t ) = 600 tan θ ...... ( 1 ) On differentiating with respect to t(time), we get y ' ( t ) = 600 sec 2 θ d θ d t d θ d t = y ' ( t ) 600 sec 2 θ d θ d t = y ' ( t ) 600 ( 1 + tan 2 θ ) ........ [ ∵ 1 + tan 2 x = sec 2 x ] d θ d t = y ' ( t ) 600 ( 1 + ( y ( t ) 600 ) 2 ) d θ d t = y ' ( t ) 600 ( 1 + y 2 ( t ) 360000 ) d θ d t =

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

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Chapter 3, Problem 77SP

To determine

To find: The rate of the angle of elevation of the TV camera.

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Chapter 3, Problem 76SP

Chapter 3, Problem 78SP

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The Eiffel Tower, in Paris France, is approximately 324 meters tall. A camera is 85 meters from the base of the tower and is moving along the horizontal ground away from the tower while keeping the top of the tower in view. What is the camera's horizontal velocity when the angle of elevation (to the top of the tower) is decreasing at 0.11 radians per second? m/s You may round your final response to two decimal places.

Chapter 3 Solutions

Calculus

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The rate of the angle of elevation of the TV camera.

Solution Summary: The author explains that the rate of the angle of elevation of a TV camera is equal to 0.012 radians per minute.

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To find: The rate of the angle of elevation of the TV camera.

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Chapter 3 Solutions