Final answer:
To calculate the golf ball's minimum linear speed to avoid being hit by the next windmill blade, we derive the time it takes for one blade to pass and then determine the speed that allows the ball to travel its own diameter within that time.
Step-by-step explanation:
Calculating the Minimum Linear Speed for a Golf Ball
To calculate the minimum linear speed at which the golf ball must move to not be hit by the next blade of the windmill, we have to consider how long it takes for one blade to move out of the way and the next one to enter the same position. Since the windmill has 12 blades and rotates with an angular speed of 1.35 rad/s, the time for one blade to pass and create space for the golf ball is the time it takes for the windmill to rotate the angle equivalent to one blade width plus one opening.
First, we find the time for one complete revolution by taking the ratio of 2π radians to the angular speed:
T = 2π / ω, where ω is the angular speed.
Then we divide T by the number of blades to find the time for one blade to pass:
t = T / 12.
Because the ball's diameter is 4.50 x 10-2 m and it has to pass through an opening of the same size, it needs to clear the space within the time t. Therefore, its minimum speed is the diameter divided by t: v = d / t.
Using these steps, we can find the required linear speed for the golf ball to avoid the next blade.