An airplane is flying in a horizontal circle at a

speed of 104 m/s. The 73.0 kg pilot does not
want the centripetal acceleration to exceed
6.98 times free-fall acceleration.
Find the minimum radius of the plane’s
path. The acceleration due to gravity is 9.81
m/s2.
Answer in units of m

V^2/R <or= 6.98*g

Solve for R. The pilot's mass is not needed.

R >or= 158 m

To find the minimum radius of the plane's path, we need to consider the centripetal acceleration and the condition given by the pilot.

The centripetal acceleration (ac) can be calculated using the formula:

ac = v^2 / r

Where:
ac = centripetal acceleration
v = velocity (speed of the plane)
r = radius of the plane's path

The condition given by the pilot states that the centripetal acceleration should not exceed 6.98 times the free-fall acceleration (g):

ac ≤ 6.98g

Substituting the values, we have:

v^2 / r ≤ 6.98g

Rearranging the equation, we can solve for r:

r ≥ v^2 / (6.98g)

Now, let's plug in the given values to calculate the minimum radius.

v = 104 m/s
g = 9.81 m/s^2

r ≥ (104 m/s)^2 / (6.98 * 9.81 m/s^2)

Simplifying the equation, we have:

r ≥ 15,197.13 m^2/s^2 / 68.6918 m/s^2

r ≥ 221.4 m

Therefore, the minimum radius of the plane's path is 221.4 meters.