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# Class Note for MATH 3331 with Professor He at UH 2

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This 13 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 15 views.

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Date Created: 02/06/15

Lecture 4 sum 2 2 smmm 5mm mmquot H sum 2 3 Mm Mam Wm M WM WW M mm m MawwmZwm 22 Applications quot Radioactive Decay 1325 jj of radioactive atoms r Model dN dtw N 0 Use A 1tnNoNt 3 VA w to determine A from mea 5 cox dN 52 N surement Solution Nt LeT Ai 0 Use t lAnNONt o Half life to determine time 75 st NODNW 6 12 1ytIzN for given N W quot N r 2 043 e ran2 21 o Natural log of ratios 3quot 1 e 7 InNON t 1f 1 I 390 5 ali 3 I Huh391 Jiwen He University of Houston Math 3331 a Section 19470 Lecture 4 January 28 2009 2 13 22 Applications 7 Exercise 2228 EX 25 After 75 4hrs 80 mg Of a 1 mg sample of Tritium remain Determine A and T12 Answer 9 a 149 n10080 0056hrs T12 In 20056 1243 hrs Jiwen He University of Houston Math 3331 39 Section 19470 Lecture 4 January 28 2009 3 13 22 Applications Exercise 2229 mmia Ex 26 T12 29mg for Techni tium 99m What remains after aims if N0 2 0g Answer A In 2 01164bxr 9 gt N9 loethgz 3549 I A h A wmrme Jiwen He University of Houston Math 3331 Section 19470 Lecture 4 January 28 2009 4 13 22 Applications Radioactive Deca Newton39s Law of Coolin Newton s L f Cpoiig Tt temperature of objet A surrounding temperature a Model dTdt A T w w u dngtz A T wdl 0 Solution see Exam9 W WW0 3 Tt Ae To A vain o T ATO Ae gt jg nTo ATt A k 1tnTo ATt A gt determine 1 t 113 nTo ATt A Ill gt determine 7 Jiwen He University of Houston Mth 3331 Section 19470 Lecture 4 January 28 2009 5 13 22 Applications Exercise Ex 33 Dead body found at t O midnight Temperature 310 1 hr later 1 am9Temperature 2900 771 Surrounding temperature A 2100 Quest on Whermid death murder occur Answer 3 1 hr To 31 T1 29 g gt 13 111 n3l 2129 21 0223hr quot Ar TH It 1 Determine time at which T 37 t 110 n l 21gtlt 1 21 deijf 211 hrs 2 2 hrs7mz n gt Death occured at 9 53 m g H Jiwen He University of Houston Math 3331 Section 19470 Lecture 4 January 28 2009 6 f 13 39 r39 Section 23 Motion of a BalI Near Surface 390 gravity Force Fg mg 70 res g32ft3298m5 I o Ach Fair 2 Rv V 395 X VeQo 17 Linear Model a L V 71 C 137 439 FFj quoti fab k I masstime I 39 A VgtO RVgtO valid for small veIOCItIes Fa Quadratic Model 1 m a m Rv kvv v F mg k masslength J v valid for larger velocities VT RVlt0 Vlt0 o We treat only the linear model 6 F ground Jiwen He University of Houston Math 3331 Section 19470 Lecture 4 January 28 2009 7 13 Section 23 2 ltIs v39 r Gravi Force and Air Resistance Motion without Air Resistance Solution of the gt 17 ha Max Height if 220 gt I 1p O v gt imax 2 max 2 a t gt22 21075 330 L we volt g Ground Hit 1 O gt i t 210 vg 2 I 73 3 v229 i 130 09 v0 2980 Impact velocnty 2 v2v82gxo w 59 votvvg gmowg WT Jiwen He University of Houston Math 3331 Section 19470 Lecture 4 January 28 2009 8 13 i Section 23 Example Example 1 Ascending balloon velocity 15ms At height 100m package is dropped When does package reach ground 9 98m52 Initial Values 330 2 100m 220 15ms gt tmam xmam Math 3331 Section 19470 Lecture 4 153 1115m 467ms 633 913 January 287 2009 Jiwen He University of Houston Gravi Force and Air Resistance i Section 23 V Solution of the Motion wit Air Resistance 1 gj kmv In CN ZZWB we showed L4 3 rya7 MO 10 5 yt yo a e ar Here y v a g 7quot l m gt Mt 2 v0 l ginMe klm gmk Integrate this to find 3 t 90t vt dt l 60 o 0M gmkxl cat sm gmkgtt mo Terminal Velocity vterm E tlim vt gmk H January 28 2009 10 13 Math 3331 Section 19470 Lecture 4 Jiwen He University of Houston Section 23 Example Example 2 see text Example 38 m 2 2kg k 4kgm g 98m32 Initial values 320 2 250m 110 0 Question Time of ground hit Impact velocity Answer Ground hit gt equation for t tg 9mk21 e mm gmW mo 2 2451 6 2 49t 250 25245 24552t 4975 Equation solver gt tg a 51525 0 Impact velocity v9 11059 496 25 1 s 47 9 ms Without air resistance 759 2mogm714s Dy 2 29mo 443ms m Jiwen He University of Houston Math 3331 Section 19470 Lecture 4 January 28 2009 11 13 7 Section 23 mple 2 Graphs forAExa 1 J 10 with aIr reSIsfance 200 39 Wlth alr reSIstance 20 39 150 39 gt 30 I x 40 l 100 39 5o 39 39 no air reSIstance 5o 39 60 39 391 no air reSIstance 0 39 39 39 7O 10 20 t 30 40 5o 0 10 20 30 4390 50 t Jiwen He University of Houston Math 3331 Section 19470 Lecture 4 January 28 2009 12 13 n Ema 2 a 13 2 my

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