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Assignment 3.pdf

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University of Guelph
MATH 2270
Matthew Demers

1 Assignment #3 Math*2270, Fall 2012 Due Wednesday, October 17 in class Instructions: ▯ Ensure that your name and ID Number are clearly printed on the front page. ▯ You are encouraged to work with your friends to complete the assignment, but please write up your ▯nal solutions on your own. ▯ Submit your assignment in class on or before the due date. ▯ This assignment carries a weight of 4% of your ▯nal grade. Late submissions will be given a zero. 1. Find the general solution for the following Bernoulli equation: x + tan(t)x = x sec (t) 2. Reduced visibility caused by particulate matter in the atmosphere is a problem, commonly referred to as haze. Diminishing visibility with distance can be quanti▯ed by a constant b, called the extinction coe▯cient, that satis▯es the equation dI ▯ = bI: dx The dependent variable I represents light intensity, as a function of independent variable x, representing distance from the light source. A beacon is lit at night in a ▯eld, measured to have a luminous intensity of 1500 candela as measured at the source (i.e. from a distance of zero). From a distance of 400 m, the intensity is measured to be 220 candela. a) Determine the value of the extinction coe▯cient b for the air in this ▯eld. 2 b) The average human can no longer detect light from a source when the intensity of the light drops to 2% of the intensity as measured at the source. If the average person were to walk away from the beacon, at what distance will they ▯rst be unable to see the light that the beacon emits? Give your answer to the nearest metre. 3. A simple hot water tank can be modeled by the following ▯rst-order di▯erential equation: cdT + 1(T(t) ▯ T ) = Q(t); dt R 0 where the dependen
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