Related Rates 4 Questions - 1 A haaehah dia111ea1d ia a...

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Unformatted text preview: 1. A haaehah dia111ea1d ia a. equate with aide [JG feet. A hatter hits the hall and tuna tewaael that haae with a. speed at 2.4 feet pet aeeeatL At what rate is hie thetaaee h'a111 aeee11d haae deel'eaah1g when he is haltwaa' ta that hate? Let a: be the distance freiii 1st base and e be the distance item 211d base. Then there is an equation: 3:2 -|- QUE = e2 when the runner is halfway te 1st, this is: 4.53 + at}? = [*2 lines = a? e a 100.623 Te find %, take derivatives ef the above equation: as ale 2 — [i=2— Ia+ Cat (mama) = menses)? gm 10.1? it I see . 151111111111, s11i11 A is 100 k111srss1 11f ship B. Ship A is ssiii11gssi1111 s1. 35 ki111111s1s1s ps1 i111111', s..111:i s11i11 B is sailing 11111111 111. 2-5 1~j111111s1s1s 111211111111. Hss issi. is the distsnss bets-sen the Ships flhfl-llsil'ls at 1:111 11111 111111. day? Let a he the distance travelled hv ship a and h be the distance travelled hv ship B. Let the distance between them be e. Then van have: (a+h]2+lflllfl=cg Using the fast that after 4 henrs a = lflfl and l:- = 140. Therefere, 2409 +1002 = e2 02 = evens e = 2a} Taking the derivative ef the eriginal eqnatien, we have: a at a. 2[a+h) (Egg) +fl=2ed—: afaafljuia-a + 313] = 233:}:- = 52133 are as _ F: g 55-38413 1-in—1ch- A ladtlel' lfl feet lnng 1'eata againat a vertical wall. If the hattunn at the ladder ah'tlea away fnnn the wall at a agreed at 2 feet per eeennd, haw faat la the angle between the tap at the ladder antl th_. wall ehangjng when the angle in radiant? Let 6' be the angle between the top ef the ladder and the well, end I the distance them the ladder te the well. Then we have: Taking derivatives: Plugging in whet we knew: it old _ 1 “mm—10 fiee_1 .5 Quit— _e em m .2828 red/see 4. The eeertlinetee at e. partiele in the 111etrie ir-y—pleiie are difiei'entiehie iuiietieiie ef time t with — —1 1T1 and = —5 Hew feet the pertiele‘t dieteiiee ii'eiii the ei'igiii '1? changing as it passes thi'eugh the paint [5,11 The thetehee between the pertiele and the erigin is given by: Taking derivatives we hate: dB nit fly — E51? + 2; m: e: ...
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