The acceleration of a descending airplane

[deveny7]

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

a_n = v² / ρ

a = √(a_t² + a_n²)

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!

 

[Ibix]

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?

 

[deveny7]

What equation could I use to include the height and downward speed as a function of time?

 

[rcgldr]

Finding the acceleration for a circular motion is easy, but I am having trouble including the downward acceleration.

You figured out the centripetal accleration, 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.