Related rates and implicit differentiation

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SUMMARY

The discussion focuses on solving a related rates problem involving a plane flying at a constant speed of 300 km/h, climbing at a 30-degree angle, and passing over a radar station at an altitude of 1 km. The solution involves using the Pythagorean theorem to relate the distances and applying implicit differentiation to find the rate at which the distance from the plane to the radar station is increasing, which is approximately 296 km/h after one minute. The key equations utilized include the Pythagorean theorem and differentiation techniques.

PREREQUISITES
  • Understanding of related rates in calculus
  • Familiarity with implicit differentiation
  • Knowledge of the Pythagorean theorem
  • Basic trigonometry, specifically angles and their relationships
NEXT STEPS
  • Study advanced applications of related rates in calculus problems
  • Learn more about implicit differentiation techniques
  • Explore real-world applications of trigonometry in physics
  • Practice solving related rates problems with varying conditions
USEFUL FOR

Students studying calculus, particularly those focusing on related rates and implicit differentiation, as well as educators looking for practical examples to illustrate these concepts.

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Homework Statement


A plane flying with a constant speed of 300 km/h passes over a ground radar station at an altitude of 1 km and climbs at an angle of 30 degrees. At what rate is the distance from the plane to the radar station increasing a minute later?

Homework Equations


a2+b2=c2

The Attempt at a Solution


I got to (y+1)2+x2=d22

It's that extra kilometer that's bothering me. It gives the answer as approx 296 km/h

d1 is the distance between the starting and current point (5 km) and d1' is 300 km/h

I don't know how to get from d1 to d2
 
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Of course, right as I post it I figure it out.

x2+y2=d12

Sub in, differentiate, solve. I'm going to leave it up, just for anyone who wants to check it out. Silly me...
 

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