A jet plane traveling 1890 km/h (525 m/s ) pulls out of a dive by moving in an arc of radius 5.20 km What is the plane's acceleration in g's?
v^2/r=525^2/5200
in "g's", divide by 9.8
5.408653846
Well, well, well, looks like this jet plane is putting on quite the performance! To determine its acceleration in g's, we can make use of the following formula:
acceleration in g's = (total acceleration) / (acceleration due to gravity)
Now, let's break it down. The total acceleration is the centripetal acceleration the plane experiences while pulling out of the dive. This can be calculated using the formula:
centripetal acceleration = (velocity^2) / radius
Plugging in the values, we have:
centripetal acceleration = (525 m/s)^2 / 5200 m
Now, we need to convert the centripetal acceleration from m/s² to g's. 1 g is approximately 9.8 m/s². So, we divide the centripetal acceleration by 9.8 m/s²:
acceleration in g's = (525 m/s)^2 / (5200 m * 9.8 m/s²)
Now, give me a moment to crunch the numbers...
*clownish mumbling and sound of a calculator clicking*
Drumroll, please! The plane's acceleration in g's is approximately 2.71 g's. Whew, that's some extreme maneuvering! Hold on tight!
To find the plane's acceleration in g's, we need to convert its acceleration into units of g, where 1 g is equal to the acceleration due to gravity (approximately 9.8 m/s²).
First, let's calculate the plane's acceleration. We know that the plane is moving in an arc of radius 5.20 km, so we can use the centripetal acceleration formula:
a = v² / r
Where:
a is the centripetal acceleration,
v is the velocity of the plane, and
r is the radius of the arc.
Given:
v = 525 m/s
r = 5.20 km = 5200 m
Substituting these values into the formula:
a = (525 m/s)² / 5200 m
a ≈ 52.5 m²/s² / 5200 m
a ≈ 0.0101 m/s²
Now, to convert this acceleration into g's, we divide it by the acceleration due to gravity (9.8 m/s²):
a_g = a / g
a_g = 0.0101 m/s² / 9.8 m/s²
a_g ≈ 0.00103 g
Therefore, the plane's acceleration is approximately 0.00103 g's.