Unlock Your Potential: Achieving the Minimum Linear Speed

How Can You Calculate the Minimum Linear Speed Required to Avoid Being Hit by a Windmill Blade?

Given a golf ball passing through a windmill with 10 blades rotating at an angular speed of 1.10 rad/s, what is the minimum linear speed needed for the ball to safely pass without getting hit?

Answer:

0.15756 m/s

Imagine yourself on a miniature golf course, facing the challenge of navigating a windmill obstacle. The key to success lies in understanding the relationship between angular speed, linear speed, and the geometry of the windmill blades.

Firstly, we know that the windmill has 10 blades, each separated by an opening equal to the width of a blade. When the golf ball reaches the edge of a rotating blade, it needs to move swiftly to avoid being struck by the next blade.

To calculate the minimum linear speed required, we start by determining the time it takes for the windmill to rotate through one blade or gap. By dividing the angle between two blades (2π/10) by the angular velocity (1.10 rad/s), we find that the time taken is approximately 0.28559 seconds.

As the ball moves, it must cover a distance equal to its diameter (4.50 x 10^-2 m) within this time frame. Using the formula Speed = Distance/Time, we calculate the minimum linear speed to be 0.15756 m/s.

Therefore, by maintaining a linear speed equal to or greater than 0.15756 m/s, you can skillfully navigate the windmill obstacle and showcase your precision and agility in the game of golf.