The Minimum Speed of a Golf Ball Passing through a Windmill
What is the minimum speed of the golf ball needed to avoid being hit by the next blade of the windmill?
The minimum speed of the golf ball must be approximately 2.52 m/s in order for it to not be hit by the next blade.
To determine the minimum speed of the golf ball so that it will not be hit by the next blade, we need to calculate the time it takes for the next blade to reach the position of the ball.
Given:
Number of blades on the windmill, n = 8
Angular speed of the windmill, ω = 266 rad/5
Diameter of the golf ball, d = 3.16 × 10^(-2) m
The time it takes for one blade to reach the position of the ball can be calculated using the formula:
Time = (2π) / ω
Substituting the given values:
Time = (2π) / (266 rad/5)
Now, we need to find the distance traveled by the ball in this time period. Since the opening between successive blades is equal to the width of a blade, the distance traveled by the ball must be equal to the width of a blade.
Distance = Width of a blade = d
The minimum speed of the ball can be calculated by dividing the distance by the time:
Speed = Distance / Time = d / [(2π) / (266 rad/5)]
Simplifying the expression:
Speed = (d * (266 rad/5)) / (2π)
Calculating the value:
Speed = (3.16 × 10^(-2) m * 266 rad/5) / (2π)
Speed ≈ 2.52m/s
In order to prevent the golf ball from being hit by the next blade of the windmill, it must travel at a minimum speed of approximately 2.52 m/s. This speed calculation is based on the diameter of the golf ball, the number of blades on the windmill, and the angular speed of the windmill.
The formula for determining the minimum speed involves calculating the time it takes for the next blade to reach the position of the ball and then finding the distance traveled by the ball in that time period. By dividing the distance by the time, we can determine the minimum speed required.
Understanding the relationship between speed, time, and distance is crucial in ensuring the safety and successful passage of objects in motion, such as the golf ball passing through the windmill. By applying these principles, we can calculate and determine the necessary speed for various scenarios and conditions.