A military jet fighter plane flying at 180m/s pulls out of a vertical dive by turning upward along a circular path
of radius 860m. What is the acceleration of the plane? Express the acceleration as a multiple ofg.
37.67
To find the acceleration of the plane, we need to use the centripetal acceleration formula:
ac = v^2 / r
where ac is the centripetal acceleration, v is the velocity of the plane, and r is the radius of the circular path.
Given that the velocity of the plane is 180 m/s and the radius is 860 m, we can substitute these values into the formula to calculate the acceleration:
ac = (180 m/s)^2 / 860 m
ac = 32400 m^2/s^2 / 860 m
Simplifying the expression, we get:
ac = 37.674 m/s^2
To express the acceleration as a multiple of g, where g is the acceleration due to gravity at the Earth's surface (approximately 9.8 m/s^2), we divide the centripetal acceleration by g:
ac = 37.674 m/s^2 / 9.8 m/s^2
ac ≈ 3.85 g
Therefore, the acceleration of the plane is approximately 3.85 times the acceleration due to gravity.
To find the acceleration of the plane, we can use the centripetal acceleration formula:
Ac = v^2 / r
where Ac is the centripetal acceleration, v is the velocity, and r is the radius of the circular path.
In this case, the velocity of the plane is given as 180 m/s, and the radius of the circular path is 860 m.
Plugging in the values into the formula, we have:
Ac = (180 m/s)^2 / 860 m
Simplifying this equation gives us:
Ac = 32400 m/s^2 / 860 m
Now, to express the acceleration as a multiple of g, we need to divide the centripetal acceleration by the acceleration due to gravity (g).
The acceleration due to gravity is approximately 9.8 m/s^2.
So, the acceleration of the plane as a multiple of g is:
Ac / g = (32400 m/s^2 / 860 m) / 9.8 m/s^2
Simplifying further, we get:
Ac / g ≈ 34.2857
Therefore, the acceleration of the plane is approximately 34.2857 times the acceleration due to gravity or 34.29g.
a=v^2/r
then number of g's is a/9.8
this is for the plane, the pilot still feels gravity, so the g's the pilot feels will be one more than the number you calculated.