Calculating Centripetal Acceleration & Time in Supersonic Airplane Turn

[BuBbLeS01]

Homework Statement

A supersonic airplane is flying horizontally at a speed of 2840 km/h. What is the centripetal acceleration of the airplane, if it turns from North to East on a circular path with a radius of 86.5 km?
How much time does the turn take?
How much distance does the airplane cover during the turn?

Homework Equations

a = v^2/r

The Attempt at a Solution

I got the acceleration which = 7.9 m/s but for calculating the time can I use Wf = Wo + at and use 90 degree for the initial and 0 for the final to solve for t

 

[bob1182006]

No I think you need to use:
$$v=\frac{2R \pi}{T}$$

where T is the time to make 1 rotation, in your problem the plane doesn't make a full rotation so the T you need will be a fraction of the original T depending on how much of a rotation the plane makes

 

[BuBbLeS01]

I am getting a really large number, 688.94 s, that doesn't seem logical?
I did...
(2 * 86500m * pi)/788.89 m/s

 

[bob1182006]

well that's to make 1 full rotation but the plane doesn't make a full rotation.
from N to E is how many degree's? or what fraction of the entire x-y plane?
take that fraction and multiply that time by it and you'll get the time to make just that part of the rotation.

 

[BuBbLeS01]

Oh okay so that's for a full revolution ok I got it then, just multiply by 1/4. Thank you.

 

[BuBbLeS01]

okay so for the third part of the question to find the distance can we use...
W = (2pi/T) * (1/4)
W = Change in theta/Change in time

 

[bob1182006]

Hm..well if the plane travel's 1/4 of the circular path that should be 1/4 of the diameter of the circle?

I've never seen those equations you're using but I've just learned circular motion from the book so far until Tuesday.

 

[BuBbLeS01]

I just tried 1/4 of the diameter but it says incorrect :( I don't know what to use.