# Airplane turning

1. Sep 30, 2007

### BuBbLeS01

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
a = v^2/r

3. 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

2. Sep 30, 2007

### 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

3. Sep 30, 2007

### 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

4. Sep 30, 2007

### 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.

5. Sep 30, 2007

### BuBbLeS01

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

6. Sep 30, 2007

### 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

7. Sep 30, 2007

### 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.

8. Sep 30, 2007

### BuBbLeS01

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