Question

In civil aviation, a "standard turn" for level flight of a propeller-driven airplane is one in which the airplane makes a complete circular turn in 2 min. If the plane's speed is 179 m/s, what is the radius of the circle? Answer in units of km. What is the centripetal acceleration of the plane? Answer in units of m/s^2.

Answer 1

`r=3418m`

`a_(cp)=9.37m/s^2`

Step-by-step explanation:

The plane makes a complete circular turn at v=179m/s in 120s, so we can calculate the circumference of this circle with C=vt since it is the distance traveled.

Since the relation between the circumference and the radius is
`C=2\pi r`, we have:

`r=(C)/(2\pi)=(vt)/(2\pi)`

Substituting our values:

`r=(vt)/(2\pi)=((179m/s)(120s))/(2\pi)=3418m`

The centripetal acceleration is then calculated using its formula:

`a_(cp)=(v^2)/(r)=((179m/s)^2)/((3418m))=9.37m/s^2`