Physics 20 Lesson 12 Reltie Motion In Lessons 10 nd 11, we lerned how to dd rious dislcement ectors to one nother nd we lerned numer of methods nd techniques for ccomlishin these ector dditions. Now we will extend the ides we lerned into ddin elocity ectors to ech other. (See es 91 to 101 in Person for n excellent discussion of reltie motion.) I. Reltie motion reference frmes Imine yourself in the followin sitution: You re on C-Trin in downtown Clry. You re stoed t sttion nd eside your trin is nother trin heded in the oosite direction which is lso t rest. As you look t the other trin, it strts to moe st you. Then you hen to look t nery lm ost nd you relize tht it ws not the other trin tht ws moin. In fct, it ws your trin tht moed while the other remined t rest. Almost eeryone hs exerienced the weird feelin of not knowin whether you re moin, or if somethin in your surroundins is moin. This is common exmle of the rincile of reltie motion. Wht you see or erceie s motion will deend on the reference frme tht you relte the motion to. The norml thins we relte motion to re the erth nd thins firmly ttched to the erth. For exmle, imine tht you re in cr heded south on Deerfoot Tril t 100 /h. This sttement is syin tht you re trelin t certin elocity reltie to the rod or reltie to the Erth. But, wht is the elocity of the rod reltie to you? Reltie to your cr, the rod is oin north t 100 /h. In similr mnner, if cr were driin st you t 10 /h reltie to your cr, wht is the other cr s elocity reltie to the rod? (Answer: 110 /h south) Exmle 1 A cr, uni-cyclist nd joer re moin st erson stndin on the round. The cr is moin est t 20 m/s reltie to the round, the uni-cyclist is moin est t 10 m/s reltie to the round, nd the joer is runnin est t 5 m/s reltie to the round. Wht re the reltie elocities of the other eole reltie to: A. The erson stndin? B. The joer? C. The uni-cyclist? D. The cr drier? cr uni-cyclist joer stndin erson Reltie to erson 20 m/s est 10 m/s est 5 m/s est 0 Reltie to joer 15 m/s est 5 m/s est 0 5 m/s west Reltie to uni-cyclist 10 m/s est 0 5 m/s west 10 m/s west Reltie to cr 0 10 m/s west 15 m/s west 20 m/s west Dr. Ron Licht 12-1 www.structuredindeendentlernin.com
II. Reltie motion winds nd currents Imine erson ddlin kyk cross still lke or ond. Since there is no motion of the wter reltie to the lnd, the motion of the kyk reltie to the wter is the sme s the motion reltie to the lnd surroundin the lke. Now imine the kyker ddlin cross moin wter like the Bow Rier. The resultin motion of the kyker will e the ddition of the motion of the kyk reltie to the wter nd the wter s motion reltie to the lnd. Birds flyin in windy conditions, swimmers crossin flowin wter in rier, or lnes flyin in windy conditions re other exmles of this tye of sitution. Exmle 2 A ird flies t 50 /h in n re where wind of 40 /h is lowin Est. Wht is the resultnt elocity of the ird when it flies? ) est ) west c) north Terminoloy for Vectors mens the ird s elocity reltie to the ir mens the ir s elocity reltie to the round mens the ird s elocity reltie to the round When the ird s elocity reltie to the ir is dded to the ir s elocity reltie to the round, the resultnt elocity is the ird s elocity reltie to the round ) The ird flyin est when 40 /h [E] wind lows will ie: = 50 /h (E) + 40 /h (E) = 90 /h (E) ) The ird flyin west when 40 /h [E] wind is lowin = 50 /h (W) + 40 /h (E) = 10 /h (W) c) The ird flyin north when 40 /h [E] wind is lowin tn = 40 /h = 38.6 E of N 50 /h 40 +50 2 2 = 64 /h = 64 /h [38.6 E of N] Dr. Ron Licht 12-2 www.structuredindeendentlernin.com
Exmle 3 An irlne flies North t 300 /h ut wind is lowin t West 70 /h ) Wht is the elocity of the lne reltie to the round? ) How fr off course will the lne e fter 3 hours? ) 70 /h o tn dj 300 /h tn o 70 /h tn dj 300 /h 1 1 o 13 W of N (70 / h) 2 (300 / h) 2 308 / h o 308 / h[13 W of N] ) the wind is the direct cuse for the lne oin off course. d = t = 70 /h (W) x 3 hours d = 210 (W) Dr. Ron Licht 12-3 www.structuredindeendentlernin.com
Exmle 4 City A is 600 south of city B. An irlne which cn fly t 200 /h reltie to the ir must fly from city B to city A. A West wind of 90 /h is lowin. ) Wht is the required hedin? ) Wht is the ctul elocity of the lne reltie to the round? c) How lon is the fliht from city B to city A? ) To comenste for the wind, the lne must fly rtly into the wind nd rtly towrd its intended destintion. The lne must fly south nd west in order to end u t city A. 200 /h 90 /h o sin hy sin o 90 sin hy 200 1 1 h h o 26.7 W of S ) The ctul elocity of the lne is equl to the djcent side of the trinle. The lne heds t 26.7 W of S so s to end u trelin striht south. (200 ) (90 ) 178.6 [S] 2 2 h h h c) The lne trels with constnt elocity thus t d 600 [S] 178.6 [S] t 3.36h h Dr. Ron Licht 12-4 www.structuredindeendentlernin.com
Exmle 5 A irl stndin on the west side of rier tht flows from north to south t 1.5 /h, wishes to swim striht cross from oint A to oint B on the dirm. She cn swim t 3.0 /h in still wter. ) Wht is the hedin she must use? ) Wht is her ctul elocity? c) If the rier is 0.25 wide, how lon would it tke her to swim cross the rier in minutes? A ) irl w 3.0 /h irl w 1.5 /h B o sin hy 1 1.5 h sin 3.0 h o 30 Nof E ) Her ctul elocity equls the djcent side of the trinle irl irl (3.0 ) 2 (1.5 ) 2 h h 2.6 [E] h c) The time required t 2.6 [E] irl d 0.25 [E] h t 0.096h or 5.76min Dr. Ron Licht 12-5 www.structuredindeendentlernin.com
III. Prctice rolems 1. Usin the Bot on Rier film foote, we cn see the effect of the reltie directions of motion of the ot nd the current. For the ske of showin clcultions with the different situtions, we shll sy tht the seed of the wter reltie to the shore is 2.0 m/s, nd the ot s seed reltie to the wter is 5.0 m/s. Sitution 1 Bot oes directly inst current Sitution 2 Bot oes directly with the current Sitution 3 Bot is imed cross rier nd is moed downstrem y the current Sitution 4 Bot wishes to o striht cross the rier comenstes for the current Dr. Ron Licht 12-6 www.structuredindeendentlernin.com
2. An ircrft hs cruisin seed of 100 m/s. On this rticulr dy, wind is lowin t 75 m/s [0 o ]. A. If the lne were to fly due north, wht would e the elocity reltie to the round? (125 m/s [37 o E of N]) B. If the ilot wishes to he resultnt direction of due north, in wht direction should he oint the lne? Wht will e the lne s dislcement in 1.25 h? (49 o W of N, 298 north) Dr. Ron Licht 12-7 www.structuredindeendentlernin.com
IV. Hnd-in ssinment 1. There re four nimls in rce (the numer in rckets indictes their to seeds); tortoise (0.2 m/s), chicken (1.5 m/s), rit (5.0 m/s) nd do (7.0 m/s). Wht is the elocity of: A. The round reltie to the chicken? B. The rit reltie to the do? C. The tortoise reltie to the chicken? D. The round reltie to the rit? E. The do reltie to the round? F. The rit reltie to the tortoise? G. The chicken reltie to the tortoise? H. The chicken reltie to the do? I. The do reltie to the do? J. The tortoise reltie to the do? 2. A trin is oin est with seed of 30 m/s. Jim nd Sm re sseners on the trin nd they re moin wy from ech other. Jim is wlkin west with seed of 1.5 m/s reltie to the trin, while Sm is runnin est t 5.0 m/s reltie to the trin. A. Wht is Jim's elocity reltie to the round? (28.5 m/s est) B. Wht is Sm's elocity reltie to the round? (35.0 m/s est) C. Wht is the trin's elocity reltie to Jim? (1.5 m/s est) D. Wht is the trin's elocity reltie to Sm? (5.0 m/s west) 3. Two othouses re locted on rier, 1.0 rt on the sme shore. Two men mke round tris from one othouse to the other, nd ck. One mn ddles cnoe t elocity of 4.0 /h reltie to the wter, nd the other wlks lon the shore t constnt elocity of 4.0 /h. The current in the rier is 2.0 /h in the strtin direction of the cnoeist. () How much sooner thn the wlker does the cnoeist rech the second othouse? () How lon does it tke ech to mke the round tri? (5.0 min; 40 min, 30 min) Dr. Ron Licht 12-8 www.structuredindeendentlernin.com
4. A do wlks t 1.6 m/s on the deck of ot tht is trelin north t 7.6 m/s with resect to the wter. () Wht is the elocity of the do with resect to the wter if it wlks towrds the ow? (9.2 m/s [N]) () Wht is the elocity of the do with resect to the wter if it wlks towrds the stern? (6.0 m/s [N]) (c) Wht is the elocity of the do with resect to the wter if it wlks towrds the est ril, t riht nles to the ot's keel? (7.8 m/s [78 o N of E]) 5. An irlne with n irseed of 400 /h is flyin south, ut n est wind of 86 /h lows the lne off course. Wht ws the ctul elocity of the lne? (409 /h [12 o W of S]) 6. Two eole cn ddle cnoe t 4.75 /h in still wter. A rier hs 2.65 /h current. A. If the cnoeists wish to ddle striht cross the rier, wht nle should the keel of the cnoe mke with the shoreline? (56 o ) B. If the rier is 0.50 wide, how much time is required to mke the journey (in minutes)? (7.6 min) 7. The ilot of ferry ot, with cruisin seed of 12 /h, wishes to sil north from Georetown, Mlysi to Medn, Indonesi cross the Strit of Mlcc. If the strit hs 3.0 /h current flowin west, wht course should the ilot set to comenste for the current? If the distnce from Georetown to Medn is 100, how lon will the silin tke? (14.5 o E of N, 8.6 h) 8. A ilot heds her lne with elocity of 255 /h north. If there is stron 112 /h wind lowin est, wht is the elocity of the lne in reference to the round? (279 /h [23.7 o E of N]) 9. A ilot wnts to fly west. If the lne hs n irseed of 95 m/s nd there is 25 m/s wind lowin north: A. In wht direction must she hed the lne? (15.3 o S of W) B. Wht will e her seed reltie to the round? (91.7 m/s) C. How fr will the lne o in 2.25 h? (743 west) 10. A 70 m wide rier flows t 0.80 m/s. A irl swims cross it t 1.4 m/s reltie to the wter. () Wht is the lest time she requires to cross the rier? (50 s) () How fr downstrem will she e when she lnds on the oosite shore? (40 m) (c) At wht nle to the shore would she he to im, in order to rrie t oint directly oosite the strtin oint? (55 o ) (d) How lon would the tri in rt (c) tke? (61 s) 11. A ycht hs cruisin seed of 45 /h nd it is heded est. If there is 20 /h current t 40 o S of E, wht is the ctul elocity of the ot? (61.7 /h [12.0 o S of E]) 12. A ilot mintins hedin due west with n ir seed of 240 /h. A ssener, who hs rduted from Physics 20, mesures the elocity of the ircrft reltie to the round nd clcultes it to e 180 /h [35 o N of W]. Wht is the mnitude nd direction of the wind? (139 /h [48 o N of E]) Dr. Ron Licht 12-9 www.structuredindeendentlernin.com