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

Answer:

1100 m

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:

• $\displaystyle v=\frac{d}{t}$  

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 $\displaystyle \frac{2\pi r}{4}$. This gives us 1/4 the circumference of a circle.

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

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

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.