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.