Circular Motion: Calculating the Diameter of a Drone's Flight Circle

What is the centripetal acceleration of a drone flying in a circular path at 35 miles per hour?

Centripetal acceleration: 0.70m/s

What is the diameter (in meters) of the circle that the drone is flying in?

Velocity: 35 miles per hour

Calculating the Centripetal Acceleration

The centripetal acceleration of the drone flying in a circular path is 0.70m/s.

Finding the Diameter of the Circular Path

To find the diameter of the circular path, we need to first calculate the velocity in meters per second.

When a boy is flying a drone in a circular path at 35 miles per hour, the centripetal acceleration experienced by the drone is 0.70m/s. This acceleration is crucial in keeping the drone moving in a circular path without flying off in a straight line. To calculate the diameter of the circle that the boy's drone is flying in, we first convert the velocity from miles per hour to meters per second.

Given that 1 mile per hour is approximately equal to 0.447 meters per second, we can convert 35 miles per hour to meters per second: 35 miles per hour * 0.447 m/s = 15.62 m/s

Once we have the velocity in meters per second, we can use the centripetal acceleration formula to find the radius of the circular path: a = v^2 / r where a is the centripetal acceleration, v is the velocity, and r is the radius.

Substituting the given values into the formula: 0.70 m/s^2 = (15.62 m/s)^2 / r

Solving for r: r = (15.62 m/s)^2 / 0.70 m/s^2 Calculating, we find r ≈ 348.47 meters Since the diameter is twice the radius, the diameter of the circle the drone is flying in is approximately twice the radius: d ≈ 2 * 348.47 ≈ 696.94 meters.