Final answer:
The average speed of the helicopter blade tip, spinning 100 revolutions per minute with a tip 5.00 m from the center of rotation, is approximately 52.3 m/s, and the average velocity over one revolution is zero because the starting and ending points are the same.
Step-by-step explanation:
To answer the student's question regarding the helicopter blade spinning at exactly 100 revolutions per minute with a tip 5.00 m from the center of rotation, we need to calculate both the average speed and the average velocity of the blade tip.
The average speed is the distance traveled per unit of time. Since the blade tip travels a circular path, we find the circumference of the circle formed by the blade's rotation and multiply it by the number of revolutions per minute. First, we calculate the circumference (C) of the circle:
C = 2πr = 2π(5.00 m) = 31.4 m
Now, since there are 100 revolutions per minute, the total distance traveled in one minute by the blade tip is 100 revolutions times the circumference of the circle:
Total distance per minute = 100 × 31.4 m = 3140 m
To find the average speed, we divide the total distance by the number of minutes:
Speed = Total distance per minute / 1 minute = 3140 m / 1 min = 3140 m/min
Converting meters per minute to meters per second:
Speed = 3140 m/min × (1 min / 60 s) = 52.3 m/s (approximately)
The average velocity over one revolution is zero because the blade tip returns to its starting point after one complete revolution, hence there is no displacement.