A 50.0-kg stunt pilot who has been diving her airplane vertically pulls out of the dive by changing her course to a circle in a vertical plane. (a) Of the plane’s speed at the lowest point of the circle is 95.0 m>s, what is the minimum radius of the circle so that the acceleration at this point will not exceed 4.00g

Respuesta :

Answer:

230.2 m

Explanation:

The centripetal acceleration of the pilot at any point in the circle is given by

[tex]a=\frac{v^2}{r}[/tex]

where

v is the speed

r is the radius of the circle

At the lowest point, the speed of the plane is

v = 95.0 m/s

We know that the maximum acceleration that the pilot can substain is

[tex]a=4.00 g = 4.00(9.8)=39.2 m/s^2[/tex]

Therefore, substituting into the equation, we can find the minimum radius of the circle so that the acceleration does not exceed this value:

[tex]r=\frac{v^2}{a}=\frac{(95.0)^2}{39.2}=230.2 m[/tex]