   Chapter 2.8, Problem 45E

Chapter
Section
Textbook Problem

# A plane flies horizontally at an altitude of 5 km and passes directly over a tracking telescope on the ground. When the angle of elevation is π / 3 , this angle is decreasing at a rate of π / 6 radians per minute. How fast is the plane traveling at that time?

To determine

To find:

The rate at which the plane is travelling.

Explanation

1. Given:

The situation is depicted in the figure below.

From the figure cotθ= x5

2. Calculations:

Differentiate it with respect to t.

csc2θdθdt=15dxdt

Substituting the values

csc2(π3

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