an airplane is flying in a horizontal of radius 1.0 km what must be the speed of the plane if the pilot is to experience a centripetal acceleration three times that of gravity.
To solve this problem, we need to use the equation for centripetal acceleration:
a = (v^2) / r,
where:
a is the centripetal acceleration,
v is the speed of the airplane,
and r is the radius of the circular path.
In this case, we want the pilot to experience a centripetal acceleration that is three times the acceleration due to gravity, which is approximately 9.8 m/s^2.
Let's calculate the centripetal acceleration required:
a = 3 * 9.8 m/s^2
= 29.4 m/s^2.
Now, we can plug this value and the given radius into the centripetal acceleration equation and solve for v:
29.4 = (v^2) / 1000,
v^2 = 29400,
v = √29400,
v ≈ 171.4 m/s.
Thus, the speed of the plane should be approximately 171.4 m/s in order for the pilot to experience a centripetal acceleration three times that of gravity.