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. What is the radius of the curve that the plane follows in making the turn

Answer 1

1100 m

Step-by-step explanation:

To solve this problem, we must note that the airplane does not make a full circle. Instead, it turns from flying east to flying south. Check the attachment for a visual of this path.

We can use this equation:

• 
  `\displaystyle v=(d)/(t)`

We are given the velocity and time of the airplane; therefore, we can solve for d in the equation.

• 
  `\displaystyle d=vt`
• 
  `\displaystyle d=(115)(15)`
• 
  `d=1725`

The distance that the airplane travels is 1725 m.

Now, using our knowledge we know that the circumference of a circle is 2πr, and this is the distance traveled for an object in a circular motion.

However, in this problem, the airplane only travels for a fourth of a circular path, so we can use
`\displaystyle (2\pi r)/(4)`. This gives us 1/4 the circumference of a circle.

This is equal to the distance (1725 m) the airplane travels:

• 
  `\displaystyle 1725=(2\pi r)/(4)`

Multiply 4 to both sides of the equation.

• 
  `6900=2\pi r`

Divide both sides by 2pi.

• 
  `r=1098.169107`
• 
  `r \approx 1100`

The radius of the curve that the plane follows in making the turn is about 1100 m.