Question

An airplane makes a gradual 90 degree turn while flying at a constant speed of 200m/s. the process takes 20 seconds to complete. fot this turn the magnitude of the average acceleration of the plane is?

Answer 1

The magnitude of the average acceleration of the plane during the turn is approximately π m/s².

Step-by-step explanation:

The magnitude of the average acceleration of the plane during the turn can be calculated using the formula for centripetal acceleration:

acceleration = (velocity2) / radius of the turn

In this case, the velocity of the plane is 200 m/s and the radius of the turn is not provided, so we need to calculate it. Since the turn is a gradual 90 degree turn, the plane would move along a quarter of a circle. We can calculate the circumference of this quarter circle using the formula:

circumference = (2 * π * radius) / 4 = π * radius / 2

Since the circumference is equal to the speed of the plane multiplied by the time taken to complete the turn:

speed * time = π * radius / 2

We can rearrange this equation to solve for the radius:

radius = (speed * time) / (π * 2)

Substituting the given values, we get:

radius = (200 m/s * 20 s) / (π * 2) ≈ 2000 m / π

Now we can calculate the average acceleration:

acceleration = (200 m/s)2 / (2000 m / π) ≈ π m/s²