Final answer:
The speed of the tip of the blade can be calculated using the formula: Speed = angular speed x radius. The angular speed can be calculated using the formula: Angular speed = 2π x frequency. The speed of the tip of the blade 10 s after the fan is turned off is approximately 0.1067 m/s.
Step-by-step explanation:
The speed of the tip of a rotating object can be calculated using the formula:
Speed = angular speed x radius
The angular speed can be calculated using the formula:
Angular speed = 2π x frequency
In this case, the fan has a diameter of 90 cm, which means the radius is half of that, or 45 cm. The angular speed can be calculated using the given rpm (revolutions per minute) of 64. Converting the rpm to rev/s by dividing by 60, we get an angular speed of approximately 1.067 rad/s. Therefore, the speed of the tip of the blade 10 s after the fan is turned off is:
Speed = 1.067 rad/s x 0.1 m = 0.1067 m/s.