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?

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

Where,

r= radius

While centripetal acceleration is defined by

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

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

PART B)

With the radius is possible calculate he centripetal acceleration,

Therefore the radius of the curva that the plane follows in making the turn is 1098.17m with a centripetal acceleration of

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

answer and explanation;