A Jet plane traveling 1800 km/h (500 m/s) pulls out of a dive by moving in an arc of radius
6.00 km. What is the plane’s acceleration in g’s?
acceleration=v^2/r units in m/s, m
then, once you have acc in m/s^2, divide by 9.8m/s to get g's
To find the plane's acceleration in g's, we need to first calculate the centripetal acceleration of the plane. Centripetal acceleration is the acceleration experienced by an object moving in a curved path, directed towards the center of the curve.
The centripetal acceleration can be calculated using the formula:
a = v^2 / r
where:
a is the centripetal acceleration,
v is the velocity of the object, and
r is the radius of the curve.
Given:
v = 500 m/s
r = 6.00 km = 6000 m
Substituting the given values into the formula, we get:
a = (500 m/s)^2 / (6000 m)
a = 250000 m^2/s^2 / 6000 m
a = 41.67 m/s^2
To convert the centripetal acceleration to g's, we can divide it by the acceleration due to gravity, which is approximately 9.8 m/s^2.
g = a / 9.8 m/s^2
g = 41.67 m/s^2 / 9.8 m/s^2
g ≈ 4.25 g's
Therefore, the plane's acceleration is approximately 4.25 g's.