The drawing shows a golf ball passing through a windmill at a miniature golf course. The windmill has 10 blades and rotates at an angular speed of 1.10 rad/s. The opening between successive blades is equal to the width of a blade. A golf ball (diameter 4.50 10-2 m) has just reached the edge of one of the rotating blades (see the drawing). Ignoring the thickness of the blades, find the minimum linear speed with which the ball moves along the ground, such that the ball will not be hit by the next blade?

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boffeemadrid boffeemadrid · Answer 1 · 2020-01-23T09:51:52+01:00

Answer:

0.15756 m/s

Explanation:

There are 10 blades and 10 gaps

To move through one blade or gap the windmill has to rotate

[tex]\dfrac{2\pi}{20}=0.31415\ rad[/tex]

This divided by the angular velocity is gives us the time

[tex]\dfrac{0.31415}{1.1}=0.28559\ s[/tex]

When the ball moves it does in a way that the ball must travel a distance of its own diameter which is [tex]4.5\times 10^{-2}\ m[/tex]

[tex]Speed=\dfrac{Distance}{Time}[/tex]

[tex]v=\dfrac{4.5\times 10^{-2}}{0.28559}\\\Rightarrow v=0.15756\ m/s[/tex]

The minimum linear speed is 0.15756 m/s