Today Mr. Max thought that going over the 3 questions we had for homework to their full extent today would be a good use of class time, and it was. So this is how to do them...
3) The paddle wheel of an old paddle wheel boat is 10m in diameter. It turns on an axis that is 1m aboth the water and spins slowly at a rate of one revolution per 6 min. The trailing edge of the paddle wheel picks up a lily pad. This lily pad travels around and around with the wheel, at times in the air and at times under water. The height of the lily pad with respect to the surface of the water varies sinusoidally with time. Sketch the graph of this sinusoidal function for one revolution starting with the lily pad at the top of the wheel. Label and number the axis appropriately. Indicate the upper and lower bounds.
a) Detemine the equation for this sinusoidal function, expressing the height of the lily pad (h) as a function of time.
b) What is the postion of the lily pad with respect to the water at a time of 14 min.
First he drew a diagram and a graph of what it was supposed to look like to give us a better idea of what was happening
He then showed us how to find what a, b, c, and d was for the sinusoidal equation y=asin(bx+c)+d
The final answer was the equation y=((pi/3)x+(pi/2))+1
If you type that into either your calculator or graphmatica your graph should look somewhat like the one sketched by Mr. Max up above.
To answer question b) you just have to trace to 14 and you should get your answer of -1.5m (under water)
For 10) you just type in the numbers on the chart given into your calculator and do
SinReg L1, L2, Y1 and then go to your graph and there should be one tracing out the temperatures. To be able to find the max temperature on your calculator you go 2nd, Trace, Maximum and find out the highest poing in the graph.
For 16) we had a big talk about the vertical and horizontal movemenit of the graph. For this equation for this question the C is 0 because you didny need to move it horizontally anymore, and the D is 21 because the graph needed to be shifted downward.
Our test is coming up quickly this Tuesday so study hard everyone!I came across something interesting that I think you guys will find interesting
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