An airplane makes a gradual 90°turn while flying at a constant speed of 200 m/s.The process takes 20.0 seconds to complete.For this turn the magnitude of the average acceleration of the plane is: A)0 m/s² B)40 m/s² C)20 m/s² D)14 m/s² E)10 m/s²

Question

Quizplus · Accepted Answer

We can use the formula for centripetal acceleration:

a = v^2/r

where v is the constant speed of the plane and r is the radius of the turn.

To find the radius, we can use the formula for the length of an arc:

s = rθ

where s is the length of the arc (in this case, the distance traveled during the turn), θ is the angle of the turn (90 degrees in this case), and r is the radius we want to find.

Since the plane completes the turn in 20 seconds, we can use the formula:

v = s/t

where t is the time taken (20 seconds in this case).

Solving for s, we get:

s = v*t = 200 m/s * 20 s = 4000 m

And solving for r, we get:

r = s/θ = 4000 m / (90 degrees * π/180) = 2222 m

Now we can substitute into the centripetal acceleration formula:

a = v^2/r = (200 m/s)^2/2222 m = 18 m/s^2

Therefore, the magnitude of the average acceleration of the plane is 18 m/s^2, which is closest to 14 m/s^2 (option D).

An Airplane Makes a Gradual 90°turn While Flying at a Constant