Question

An airplane flying at 115 m/s due east makes a gradual turn following a circular path to fly south. The turn takes 15 seconds to complete. a. What is the radius of the curve that the plane follows in making the turn? b. What is the magnitude of the centripetal acceleration during the turn?

Answer 1

To solve this exercise it is necessary to apply the concepts related to Centripetal and Perimeter acceleration of a circle.

The perimeter of a circle is defined by

$P = 2\pi r$

Where,

r= radius

While centripetal acceleration is defined by

$a=\frac{v^2}{r}$

Where,

v= velocity

r= radius

PART A)

The distance of a body can be defined based on the speed and the time traveled, that is

x = v*t

For our values the distance is equal to

x = 15*115=1725m

The plane when going to make the turn from east to south makes a quarter of the circumference that is

$\frac{P}{4} = \frac{2\pi r}{4}$

The same route you take is the distance traveled, that is

$x = \frac{P}{4}$

$x = \frac{2\pi r}{4}$

$1725 = \frac{2\pi r}{4}$

$r = 1098.17m$

PART B)

With the radius is possible calculate he centripetal acceleration,

$a = \frac{v^2}{r}$

$a = \frac{115^2}{1098.17}$

$a = 12.04m/s^2$

Therefore the radius of the curva that the plane follows in making the turn is 1098.17m with a centripetal acceleration of $12.04m/s^2$