“The great calculus II Conundrum” Background: It is the year 2030.The Characters

Question

“The great calculus II Conundrum”

Background:

It is the year 2030.The Characters In this murder mystery were classmates at the United States and graduated in the year 2000. All were advanced placed Calculus II students the first semester of their freshman year. They retired as Lt Colonels and started a small business named “ITSI” (Innovative Techniques for solving Integrals).The business folded after five years and the four partners went their separate ways (although they kept in contact with each other as all alumni do). The four characters are: Lt Col Taylor, Lt Col Riemann, Lt Col Trapezoid, and Lt Col Euler. As all four prepare to gather to meet tonight at Lt Col’s Euler’s cabin outside of Colorado Springs, we find that Lt Col Euler has been murdered –the other three Lt Cols are the primary suspects.

Clue 3: We know the body was found under water. We know about 17690 foot pounds of work was required to pump out all of the standing water. Where was the body found?

a.At the bottom of the well. The well was cylindrical with a radius of 3.385 feet and a depth of 18 feet. The standing water in the well had a depth of 3.5 feet and the pump was located at ground level.

b.At the bottom of the lap pool. The lap pool was rectangular (6 ft*30ft)and had a depth of 4 ft. The pool was filled to the 3.5ft mark and the pump was located on the pool deck.

c.At the bottom of the “cold” hot tub. The hot tub was square (6ft*6ft) and had a depth of 4 feet. The hot tub was filled to the 3.5foot mark and the pump was located on the hot tub deck.

Explanation / Answer

c)

Area of the base = 6*6 = 36

Now, the depth is 4

So, the distance that the water has to be moved is (4 - x)

Volume = 36(4 - x)

Now, MAss = Density * volume

Mass = 62.5 * 36 * (4 - x)

Now, work = Mass * distance

W = 62.5 * 36 * (4 - x) * dx

Now, the total height of the water is from x = 0 to x = 3.5

So, integrate this over 0 to 3.5 :

(integral 0 to 3.5) 62.5 * 36 * (4 - x) * dx

gives us

17718 ft pds approx

So, C checks out!

Option C

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