What is the minimum speed?...?

Question

A mini-golf course has a windmill that blocks the opening lower level of the course. The windmill has 4, 2 m long blades that are 25 cm wide at the ground and complete 2 revolutions per minute. If the ball starts from rest 10 meters away, what is the minimum speed with which you must strike the ball on level ground in order to have it pass between the blades?

Answer 1

You must hit the ball as soon as one of the blades is vertical with the ground.

The distance between the blades you can find using an arc length equation. (Remember to use radians. There are 90 degrees between blades so pi/2 radians.)

D = 2*pi/2 = pi m

However, that is from the center of one blade to the other, so the distance from edge to edge = pi - 0.25 m
In radians, to figure the distance from one edge to another use the arc length aganing
theta = (pi-0.25)/2

The period of the blades are 2 rpm
w = 2 revs/min = 2* 2*pi rad/rev * 1/60 min/sec

Using rotational kinematics to find the time
theta = w*t
t = theta/w

Know you know how much time you have between blade edges. Use that time to figure out how much velocity the ball needs to get that far.

V = 10/t m/s.

Just plug and chug.