The acceleration of a descending airplane

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Homework Help Overview

The problem involves an airplane descending in a circular pattern, with specified horizontal and vertical speeds, as well as an increasing downward acceleration. The context is centered around understanding the components of acceleration in circular motion.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss how to incorporate both the centripetal and downward accelerations into a single acceleration vector. Questions arise regarding the formulation of the airplane's position as a function of time and how to derive acceleration from first principles.

Discussion Status

Some participants have offered guidance on considering the components of acceleration and suggested methods for calculating the overall magnitude. There is an ongoing exploration of how to effectively combine the horizontal and vertical components of acceleration.

Contextual Notes

Participants note the challenge of integrating the downward acceleration with the circular motion parameters, highlighting the need for clarity on the relationship between height, speed, and acceleration over time.

deveny7
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Homework Statement



An airplane descends in a circular pattern with a constant radius of 250 meters. The airplane has a horizontal speed of 75 m/s (constant) and a downward
speed of 5 m/s, which is increasing at a rate of 2 m/s2

Determine the acceleration of the airplane.


Homework Equations



an = v2 / ρ

a = √(at2 + an2)


The Attempt at a Solution



Finding the acceleration for a circular motion is easy, but I am having trouble including the downward acceleration. Any help is greatly appreciated!
 

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If all else fails, derive it from first principles.

Assuming that the aircraft is at height h and is circling the origin, can you write down its position as a function of time? If so, what's its acceleration?
 
What equation could I use to include the height and downward speed as a function of time?
 
deveny7 said:
Finding the acceleration for a circular motion is easy, but I am having trouble including the downward acceleration.
You figured out the centripetal acceleration, and the problem states the downwards acceleration is 2 m / s2, which would be the components of the acceleration vector (horizontal and vertical). To get the magnitude, take the square root of the sum of the squares of the components.
 

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