Question

An acrobatic airplane performs a loop at an airshow. The centripetal acceleration the plane experiences is 14.7 m/s2. If it takes the pilot 45.0 seconds to complete the loop, what is the radius of the loop? Round your answer to the nearest whole number.

Answer 1

The radius of the loop is approximately 285 meters.

Step-by-step explanation:

To find the radius of the loop, we can use the formula for centripetal acceleration:

ac = v^2 / r

where v is the velocity and r is the radius. We are given the centripetal acceleration as 14.7 m/s^2. We also know that the time taken to complete the loop is 45.0 seconds.

Since the loop is a full circle, the distance traveled is equal to the circumference of the circle, which is 2πr. We can use this information to find the velocity:

v = 2πr / t

Substituting the values we have, we get:

14.7 = (2πr / t)^2 / r

Rearranging the equation, we find:

r = t^2 * ac / (4π^2)

Plugging in the values, we have:

r = 45^2 * 14.7 / (4π^2) ≈ 285

Therefore, the radius of the loop is approximately 285 meters.