Question

The blades on a model windmill take 4 seconds to make a full rotation. At the lowest point, the tip of the blade is 0.5m off the ground, and at the highest point the tip of the blade is 2.5m off the ground

sketch a graph of height against time to show the distance between the tip of the blade and the ground for 2 complete rotations. at time zero, the blade is pointing straight down. clearly label the scale of both axes

Answer 1

So if at time 0 the blade is pointing straight down, then this would also mean that at time 0 the blade is at it's lowest, 0.5m off the ground. Also, if the windmill takes 4 seconds to go around 360degrees, then, logically, halfway through that 4 seconds the blade would be pointing straight up. So that being said, we can say t = 0 is 0.5m, t = 2 (half of 4) is 2.5m. Another thing that can be assumed is that the windmill would keep spinning. This means that every 4 seconds the blade will be 0.5m and at the blade will be at its highest at 2 seconds and every additional 4 seconds after that, All of that kinda make sense so far?

Answer 2

yes it does

Answer 3

@Psymon, it's great to see you helping with this question. My advice to you is to also utilize the drawing tool to create a visual representation of the graph of the blade. This would also help other users who may visit the question to try to understand it.

Answer 4

I'll draw it out, just concept stuff I guess xD

Answer 5

So before we actually draw, just want to make sure we know what goes where and why. So we need to put this on a graph in terms of x and y. Y is called a dependent variable because it's value changes based on what value you give to x. So for this problem, the position of the blade is dependent on the amount of time elapsed. This means that we have to make sure that we graph time along the x-axis and the position in height along the y-axis. You may have known this, but wanted to get that out of the way in case :P

Answer 6

lol, thanks for the reminder :P

Answer 7

Now of course, this gives a lot of the graph away, but best to make sure we know where everything should be instead of just drawing a line through. Now, because we know how long it takes for the blade to spin once, 4 seconds, we canbreak that apart into as many equal segments as we feel are needed. Maybe we want to be ablle to plot 8 positions of the blade during those 4 seconds. Well, we've already said that at 2 seconds the blade will be at its max. Well, if we then half that amount of time to 1 second, the blade will be only halfway up. And if we half that amount of time to 0.5 seconds, the blade will be 1/4 of the way up. Basically, its very easy to pick spots for the rest of the graph by just cutting up the movements into divisions of 2. We don't need 8, though, we can just plot 4 per :P