(Distance between aircraft) An aircraft is 144 km east of an airport and is travelling west at 2

Name: Problem 31, Chapter 4: Calculus: A Complete Course
Uploaded: 2021-12-02T12:29:17-08:00
Duration: 2 min 11 s
Channel: Narayan Hari
Description: (Distance between aircraft) An aircraft is 144 km east of an airport and is travelling west at 200 km / h. At the same time, a second aircraft at the same altitude is 60 km north of the airport and travelling north at 150 km / h. How fast is the distance between the two aircraft changing?

step 1 In this problem first I'm drawing the diagram so just look at it carefully after that I solve it

Question

(Distance between aircraft) An aircraft is $144 \mathrm{km}$ east of an airport and is travelling west at $200 \mathrm{km} / \mathrm{h}$. At the same time, a second aircraft at the same altitude is $60 \mathrm{km}$ north of the airport and travelling north at $150 \mathrm{km} / \mathrm{h}$. How fast is the distance between the two aircraft changing?

   (Distance between aircraft) An aircraft is $144 \mathrm{km}$ east of an airport and is travelling west at $200 \mathrm{km} / \mathrm{h}$. At the same time, a second aircraft at the same altitude is $60 \mathrm{km}$ north of the airport and travelling north at $150 \mathrm{km} / \mathrm{h}$. How fast is the distance between the two aircraft changing?

Calculus: A Complete Course

Robert Adams ,… 9th Edition

Chapter 4, Problem 31

Instant Answer

Solved by Expert Narayan Hari

12/02/2021

Step 1

Let's denote the airport as point O, the first aircraft as point P, and the second aircraft as point Q. The distance between the two aircraft is denoted as d. The distance of the first aircraft from the airport is x and the distance of the second aircraft from the Show more…

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(Distance between aircraft) An aircraft is $144 \mathrm{km}$ east of an airport and is travelling west at $200 \mathrm{km} / \mathrm{h}$. At the same time, a second aircraft at the same altitude is $60 \mathrm{km}$ north of the airport and travelling north at $150 \mathrm{km} / \mathrm{h}$. How fast is the distance between the two aircraft changing?

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Key Concepts

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Related rates problems involve calculating the rate at which one quantity changes by relating it to other quantities whose rates of change are known. Typically, the variables in a problem are connected through an equation, and differentiation with respect to time allows determination of the unknown rate.

Pythagorean Theorem

The Pythagorean theorem is used to relate the distances along perpendicular axes. In problems involving positions in a plane, it provides the relationship between the horizontal and vertical distances and the hypotenuse (direct distance) between two points.

Implicit Differentiation

Implicit differentiation is a technique used when an equation defines a relationship between variables that are functions of time. By differentiating both sides of the equation with respect to time, one can solve for the derivative of a variable even when it is not isolated, making it essential for solving related rates problems.

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