Related Rates Problem (Calc 1)

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SUMMARY

The discussion focuses on solving a related rates problem in calculus involving a plane flying at an altitude of 5 km and a tracking telescope. When the angle of elevation is π/3 and decreasing at a rate of π/6 rad/min, the goal is to determine the speed of the plane. Participants emphasize the importance of visualizing the problem by drawing a right triangle, where the vertical leg represents the altitude and the horizontal leg represents the distance from the telescope to the plane.

PREREQUISITES
  • Understanding of related rates in calculus
  • Knowledge of trigonometric functions and their derivatives
  • Ability to draw and interpret right triangles
  • Familiarity with the concept of angle of elevation
NEXT STEPS
  • Study the application of related rates in calculus problems
  • Learn how to derive relationships between angles and sides in right triangles
  • Practice solving similar problems involving angles of elevation and horizontal motion
  • Explore the use of derivatives in real-world motion scenarios
USEFUL FOR

Students studying calculus, particularly those focusing on related rates, as well as educators looking for examples to illustrate these concepts in a classroom setting.

niravana21
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Homework Statement


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 rad/min. How fast is the plane traveling at that time?

The Attempt at a Solution


I can't seem to visualize this problem :(

Thanks!
 
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niravana21 said:

Homework Statement


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 rad/min. How fast is the plane traveling at that time?

The Attempt at a Solution


I can't seem to visualize this problem :(

Thanks!

Draw a right triangle with the telescope at the Pi/3 angle and 5km as the vertical leg. You are looking for the rate of change of the horizontal leg of this triangle, so you need to write an equation relating it to the known angle and height.
 

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