Chapter 2.6, Problem 26E

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11th Edition

Ron Larson + 1 other

ISBN: 9781337275347

Textbook Problem

Air Traffic Control An airplane is flying at an altitude of 5 miles and passes directly over a radar antenna (see figure). When the plane is 10 miles away

To determine

**To calculate:** The speed of the plane when the plane is 10 miles away from the radar and its distance from the radar is changing at a rate of 240 miles per hour.

Explanation

**Given:**

An airplane is flying at an altitude of5 miles and passes directly over a radar antenna as shown in the figure. When the plane is 10 miles away, the radar detectsthat the distance *s* is changing at a rate of 240 miles per hour.

**Formula used:**

The Pythagoras theorem for a right-angled triangle with hypotenuse *h* and other two sides,

If, *u* and *x*, then *x* and,

The derivative of the function,

**Calculation:**

The rate at which the distance *s* is changing is:

The value of *s* can be calculated by applying Pythagoras theorem in the triangle given below:

Applying the Pythagorean Theorem in the above triangle, we get

Now, we will differentiate the above equation with respect to *t*.

The derivative of a constant is zero

Sect-2.1 P-1ESect-2.1 P-2ESect-2.1 P-3ESect-2.1 P-4ESect-2.1 P-5ESect-2.1 P-6ESect-2.1 P-7ESect-2.1 P-8ESect-2.1 P-9ESect-2.1 P-10E

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P-57RECh-2 P-58RECh-2 P-59RECh-2 P-60RECh-2 P-61RECh-2 P-62RECh-2 P-63RECh-2 P-64RECh-2 P-65RECh-2 P-66RECh-2 P-67RECh-2 P-68RECh-2 P-69RECh-2 P-70RECh-2 P-71RECh-2 P-72RECh-2 P-73RECh-2 P-74RECh-2 P-75RECh-2 P-76RECh-2 P-77RECh-2 P-78RECh-2 P-79RECh-2 P-80RECh-2 P-81RECh-2 P-82RECh-2 P-83RECh-2 P-84RECh-2 P-85RECh-2 P-86RECh-2 P-87RECh-2 P-88RECh-2 P-89RECh-2 P-90RECh-2 P-1PSCh-2 P-2PSCh-2 P-3PSCh-2 P-4PSCh-2 P-5PSCh-2 P-6PSCh-2 P-7PSCh-2 P-8PSCh-2 P-9PSCh-2 P-10PSCh-2 P-11PSCh-2 P-12PSCh-2 P-13PSCh-2 P-14PSCh-2 P-15PS

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