Chapter 11.4, Problem 36E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

** Distance** Two boats leave the same port at the same time, with boat A traveling north at 15 knots (nautical miles per hour) and boat B traveling east at 20 knots. How fast is the distance between them changing when boat A is 30 nautical miles from port?

To determine

**To calculate:** How fast is the distance between the boats changing when boat A is

Explanation

**Given Information:**

Boat A is

**Formula used:**

According to the Pythagoras theorem,

Where

According to the chain rule differentiation, if *y* is a differentiable function of *x.*

The derivative of a constant value, *k*, is

According to the sum rule of differentiation, if a function is of the form

**Calculation:**

As it is provided that boat A is

Thus, this arrangement can be considered as a right angled triangle with the distance between the boats as hypotenuse and the distance of boat A from the port be the altitude and distance of boat B from the port be the base of the triangle.

Now, let

So,

Differentiate the equation (1) with respect to

Now, the rate at which the distance between the boats is changing when A is

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