Final answer:
The toy airplane's speed is calculated to be 1.5089 m/s, and its centripetal acceleration is found to be 1.265 m/s² by using the formulas for circumference, speed, and centripetal acceleration with the given information.
Step-by-step explanation:
Calculating the Speed and Centripetal Acceleration of a Toy Airplane
To find the speed of the toy airplane, we must first determine the distance it travels per revolution and then multiply it by the total number of revolutions. The distance for one revolution is the circumference of the circle (Distance = 2πr). Using the given radius of 1.8 m, we calculate the circumference: Distance = 2π(1.8 m) = 11.31 m. Since the airplane makes 24 revolutions, the total distance is 24 × 11.31 m = 271.44 m.
The total time the airplane flies is 3 minutes, which is 180 seconds. Speed is distance divided by time, so Speed = 271.44 m / 180 s = 1.5089 m/s. The centripetal acceleration (ac) is given by the equation ac = v2/r, where v is the speed and r is the radius. Substituting the values we have, the centripetal acceleration is ac = (1.5089 m/s)2 / 1.8 m = 1.265 m/s².