Calculus Help!

[WillyPorts]

Hi everyone I'm new to these forms. I have attached a pdf of a writing project I'm working on in my Calc 3 class. I'm just trying to find somewhere to start, because I'm kind of lost. Most of the Calc 3 class has been based on multivariable calculus and objects in 3-d.

 

The problem states that I must determine how much solar energy will be lost because of the shadows. I must calculate the fraction of energy being lost.

 

We have not studied the loss of energy. I've tried searching google and I have only found complex equations. Is there a simple formula for energy lost?

 

One way I was thinking about solving this problem would be to first calculate the time it takes for all the shadows to make one complete cycle. Then I would calculate the time it takes the shadow to pass over the solar panel. This could be calculated by using the 3-d distance formula, and once the distance is found it could be multiplied by the speed of a shadow. After this I could divide the time for the shadow to pass over the solar panel by the total time, giving the fraction of energy lost.

 

Is this the right approach to this problem? This may be an obvious question, but how do I differentiate the straight lines from the arcs? Also, how does the degree the line passing through the solar panel oriented at approximately 24.6 degrees west of due north do anything to this problem?

 

I don't have to meet with the teacher until this Friday and the actual project is due next Friday.

 

Any help will be greatly appreciated.

Thank you!

calc.pdf

Edited November 8, 2011 by WillyPorts

[Cap'n Refsmmat]

The fraction of energy lost will merely be the fraction of the solar panels which are covered in shadow at any given moment; there isn't a special equation for that.

[DrRocket]

Hi everyone I'm new to these forms. I have attached a pdf of a writing project I'm working on in my Calc 3 class. I'm just trying to find somewhere to start, because I'm kind of lost. Most of the Calc 3 class has been based on multivariable calculus and objects in 3-d.

 

The problem states that I must determine how much solar energy will be lost because of the shadows. I must calculate the fraction of energy being lost.

 

We have not studied the loss of energy. I've tried searching google and I have only found complex equations. Is there a simple formula for energy lost?

 

One way I was thinking about solving this problem would be to first calculate the time it takes for all the shadows to make one complete cycle. Then I would calculate the time it takes the shadow to pass over the solar panel. This could be calculated by using the 3-d distance formula, and once the distance is found it could be multiplied by the speed of a shadow. After this I could divide the time for the shadow to pass over the solar panel by the total time, giving the fraction of energy lost.

 

Is this the right approach to this problem? This may be an obvious question, but how do I differentiate the straight lines from the arcs? Also, how does the degree the line passing through the solar panel oriented at approximately 24.6 degrees west of due north do anything to this problem?

 

I don't have to meet with the teacher until this Friday and the actual project is due next Friday.

 

Any help will be greatly appreciated.

Thank you!

 

 

Unfortunately the key piece of information required is contained in this sentence describing the figure in your attachment -- "The line passing through our solar panel appears is oriented at approximately 24:6 degrees west of due north." -- which makes no sense.

 

I have long thought that proficiency in the English language should be a prerequisite for calculus. It appears that it should also be enforced as a requisite for those teaching calculus.

[imatfaal]

Frankly I would like to hire the Big Ideas Group architects regardless - the six shadows (200m across) trace the same route regardless of the time of day or height of the sun at noon (ie time of year); that's not a sculpture it's the eight wonder of the modern world!

 

You have the length of the path, and the rate at which each shadow passes - so you can work out a period from one shadow touching the NW edge of the solar panel to the next shadow touching the NW edge of the solar panel.

 

this period will be x seconds - a proportion of this period x_clear there will be no occlusion and a second period x_shadow in which there will be a varying amount of shadow over the panel. you will have to model this shadow in time as ratio of the total area of the panel (first thoughts would be as two segments of a circle). once you have a time-varying equation for the amount of the panel that is in shadow during x_shadow then you can work out the overall exposure in x_shadow.

 

I have no real idea why they included the bearings and agree with Doc Rock that it isn't worded nicely