How Fast Must a Golf Ball Travel to Avoid Windmill Blades?

[Crazedkid]

ok i need help understanding were to start with this problem. any hint would be appreciated

A windmill has 8 blades abd rotates at an angular speed of 1.25 radians/second. The opening between succesive blades is equal to the width of a blade. A golf ball of diameter 4.50*10 -2m is just passing by one of the rotating blades. What is the minimum speed of the ball so that it will not be hit by the next blade?


I am soooo lost

 

[Leo32]

Maybe start with how wide the gap between the blades is, expressed in radians...

 

[CartoonKid]

Yup, first you have to find the angular distance of the opening. Since the question says that the opening is equal to the width of the blade, it implies that the $$\Theta=\frac{2\pi}{16}$$. With the $$\Theta$$ and the angular speed, you can find out the time needed for the blade to cover this distance. For the golf ball to travel at minimum speed through the opening, you have to assume that the ball is right at the beginning of an opening before it passes through. Then it's easy to see that for the ball to pass through the opening, the distance that it needs to travel should be equal to at least its diameter. With the time you found and the known distance, you will find the answer.

 

[Crazedkid]

thankyou very much for your help