How to Calculate the Minimum Speed of a Golf Ball Passing Through a Windmill

What is the minimum speed required for a golf ball to pass through a windmill without being hit by the next blade?

The minimum speed required for a golf ball to pass through a windmill without being hit by the next blade is 0.1432 m/s.

When a golf ball passes through a windmill with 8 blades rotating at an angular speed of 1.25 rad/s, the ball must have a minimum speed to ensure it does not get hit by the next blade. To calculate this minimum speed, we can use the formula:

\[ v = \frac{d_{ball}}{\Delta t} \]

Where:

\( d_{ball} \) = Ball diameter

\( \Delta t \) = Space time

The angle swept out by either a blade or space between them is given by:

\( \theta = \frac{2\pi}{16} = \frac{\pi}{8} \, rad \)

By using the angular velocity formula \( \omega = \frac{\theta}{t} \), we can calculate the time \( t \) taken for the ball to pass through the windmill:

\( t = \frac{\theta}{\omega} \)

\( t = \frac{\pi/8}{1.25} = 0.3141 s \)

Therefore, the minimum speed of the golf ball can be calculated as:

\( v = \frac{4.50 \times 10^{-2} \, m}{0.3141 \, s} = 0.1432 \, m/s \)

So, the minimum speed required for the golf ball to pass through the windmill without being hit by the next blade is 0.1432 m/s.