#2 When blade 1 is vertical, blades 2 and 3 are at angles 30 and 150
#3 when blade 2 is 7m above the axle, then its angle from the vertical is arccos(7/8). Blade 3 is 120 degrees from that angle.
#4 If you mean the blades are rotating at 60°/s = π/3 rad/s, then since s = rθ, their tips are moving at 8π/3 m/s
Assuming the ball is thrown far from the axle, so its size is relatively small compared with the gap, then since the blades are 120° apart, they take 2 seconds to move from one position to the next.
See what you can do with this info...
Question:
A wind turbine has a total height of 50m, with 3 equally spaced blades that are 16m in diameter.
1) Create equations modelling the height of points on the tips of blades One, Two and Three. Graph these three curves on one graph.
[Answers: Blade 1: y=8sin(x)+42
Blade 2: y=8sin(x+120)+42
Blade 3: y=8sin(x-120)+42]
2) Maintenance can only be done on the blades when the points on blades Two and Three are at the same height. Identify the rotation angles when this would occur as well as the height of the points at that time.
3) What is the height of the tip of Blade Two, when the tip of Blade Three is 1m below its maximum height?
4) On a particular day the blades are rotating at a rate of 60 per second. How fast are the tips of the blades travelling? If you wanted to throw a tennis ball through the blades and not be struck, how long is the gap of time between blades?
I'm just so freaking lost on how to answer 2, 3 and 4. I have the equations for the first question, but have no idea how to find the answers for the three others. I've been stuck on this for over an hour. I think I'm just overcomplicating how to answer them, which is why I'm stuck, and if anyone could please point me in the right direction, I'd be super thankful.
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