Unit 5: Vectors. Scalar Quantity: - quantity that involves a Magnitude of measurement but NO Direction.

Transcription

1 pplied Mth 0 Unit 5: Vectrs Unit 5: Vectrs 7-: Vectrs nd clrs clr Quntit: - quntit tht inles Mgnitude f mesurement but O Directin. Vectr Quntit: - quntit tht inles Mgnitude f mesurement D Directin. clr Quntities Emples Vectr Quntities Emples Distnce 0 m Displcement 0 m [rth] (Length WITHOUT Directin) (Length WITH Directin) peed 50 km/h Velcit 50 km/h [80 ] (Hw st n bject mes WITHOUT Directin) (Hw st n bject mes WITH Directin) Mss 44 kg rce 40 dwnwrd (Hw Much tuff is I n bject) (Mss ccelertin) Energ 500 kj Weight 500 (lws dwnwrd) (Emits in LL Directins) (rce due t Grit) Temperture 5 rictin 5 (ginst the directin f mtin) (erge Kinetic Energ f n bject) (esistnce rce due t urfce nditins) Time 65 minutes ccelertin 5 m/s [W] (Hw st Velcit hnges er Time) Vectr ttin: - methd f indicting tht the quntit is ectr b plcing n rrw n tp f the rible. ering: - cmpss bering TT t the rth (0 ) nd rttes LOKWIE. W 5 0 E 45 Emple: Vectr r 0 km/h [E] r 45 E (rm, me 45 twrds E) Ending Pint (Hed) W 70 E 90 Mgnitude 0 km/h W 5 80 E 5 trting Pint (Til) prighted b Gbriel Tng.Ed.,.c. Pge 09.

2 Unit 5: Vectrs pplied Mth 0 Drw Vectrs with Prper cle Emple : Drw 60 [5 ] Emple : Drw 45 [40 ] (Use cm 0 ) (Use cm 0 ) cm 4.5 cm Emple : Drw d km [0 W] Emple 4: Drw d 56 m [E5 ] (Use cm 0 km) (Use cm 0 m) d km. cm 0 d 56 m cm W 70 5 E O we cn s d km [W70 ] O we cn s d 56 m [55 E] Equl nd Oppsite Vectrs Equl Vectrs: - ectrs tht he the ME Mgnitude D Directin. D D where D nd the he the ME Directin. Pge 0. prighted b Gbriel Tng.Ed.,.c.

3 pplied Mth 0 Unit 5: Vectrs Oppsite Vectrs: - ectrs tht he the ME Mgnitude but DIEET Directin. D where D nd the he OPPOITE Directin. D Emple 5: Drw the ppsite elcit ectr t 40 km/h [6W ] 40 km/h (Use cm 0 km/h) 6 4 cm W E 40 km/h 4 cm 6 Oppsite Velcit Vectr 40 km/h [6 E] Emple 6: Drw the ppsite ccelertin ectr t 55 m/s [5 ] (Use cm 0 m/s ) 55 m/s 5.5 cm W 5 E Oppsite ccelertin Vectr 55 m/s [95 ] m/s 5.5 cm 7- ssignment: pg # t 9 prighted b Gbriel Tng.Ed.,.c. Pge.

4 Unit 5: Vectrs pplied Mth 0 7-: dding Vectrs Using cle Digrms esultnt Vectr: - the ectr tht is the result f ectr dditin r subtrctin. - frm the trting Pint f the irst Vectr t the Ending Pint f the Lst Vectr. dding Vectrs (lws nnect Vectrs OM HED TO TIL) u + u lide ectr lng ectr u until the ectrs re lined up rm HED t TIL. u Emple : Drw + D D D D D ubtrcting Vectrs (DD OPPOITE VETO) u ( ) u u + rete n Oppsite Vectr ( ) u dd rm HED T TIL u Emple : Drw D D D D D D D D D + ( D) Pge. prighted b Gbriel Tng.Ed.,.c.

5 pplied Mth 0 Unit 5: Vectrs Emple : ship left the dck nd treled nrth t 50 km/h fr hurs, then it turned west t 60 km/h fr hur.. Wht is the net resultnt displcement ectr,? (Use cm 0 km) d 50 km/h [] hr d 00 km [rth] d 60 km/h [] hr d 80 km [West] (5 cm) (9 cm) mesured (0. cm) d 80 km [West] (9 cm) 0. cm 0 km/cm 06 km mesured ngle (6 ) d 00 km [rth] (5 cm) 06 km [6 W] r [W9 ] r [99 ] ering b. Wht is the displcement ectr the ship must fllw t return t the dck? ering (r ) 9 E 9 eturn Displcement Vectr Oppsite esultnt Vectr 06 km 06 km [6 E] r [E9 ] r [9 ] Emple 4: plne is fling suth t 400 km/h nd sted wind is blwing frm the est t 00 km/h. If sudden gust f wind ppers frm the suth t 50 km/h. Wht is the resultnt elcit ectr f the plne? (Use cm 00 km/h) 00 km/h [West] (frm the est) ( cm) mesured ngle ( ) ering km/h [uth] (4 cm) 50 km/h [rth] (frm the suth) (.5 cm).7 cm 00 km/h / cm 70 km/h km/h [uth] (.5 cm) 00 km/h [West] 70 km/h [ W] r [W68 ] r [0 ] prighted b Gbriel Tng.Ed.,.c. Pge.

6 Unit 5: Vectrs pplied Mth 0 Emple 5: kk left Prt lberni due west fr 5 km. It then turned t bering f 00 nd treled n fr 40 km. Hering the sighting f killer whles, it turned t bering f 40 fr 0 km. Wht is the kk s net displcement frm Prt lberni? (Use cm 5 km) ering 40 mesured (.0 cm).0 cm 5 km/cm d 0 km [40 ] ( cm) 60 km 60 km [W8 ] r [6 W] r [98 ] d 40 km [00 ] (8 cm) mesured ngle (8 ) ering 00 d 5 km [West] (5 cm) ering Equilibrnt: - the ppsite resultnt frce f n bject which des nt me, but is cted n b ther frces. Emple 6: Tw tw trucks re tring t pull he triler ut f ditch. One tw truck is ppling frce f 4500 t 40 W nd the ther truck is pulling with frce f 6500 t 0. The triler remined stuck in the ditch.. lculte the resultnt frce n the he triler. (Use cm 000 ) 4500 [40 W] (4.5 cm) 40 W 6500 [0 ] ering 0 mesured ngle (0 ) mesured (6.6 cm) ering cm 000 /cm [0 ] (6.5 cm) 6600 [W0 ] r [70 W] r [50 ] Pge 4. prighted b Gbriel Tng.Ed.,.c.

7 pplied Mth 0 Unit 5: Vectrs b. Wht is the equilibrnt frce n the he triler? ering 70 Equilibrnt rce Oppsite esultnt rce E 6600 [E0 ] r [70 E] r [70 ] Emple 7: nen sign hs weight f 500 is hnged b tw rpes s shwn belw. One rpe with tensin frce f 500 is directed t the left with n ngle f 40 t the hrizntl. Determine the tensin frce ectr eerted b the ther rpe t keep the nen sign frm ming. (Use cm 500 ) 40 en ign [40 hrizntl] ( cm) Hrizntl? [ngle t the hrizntl] Hrizntl Hrizntl mesured (.8 cm).8 cm 500 /cm 900 Weight ( W ) 500 [Up] (5 cm) (5 ) mesured Weight (W ) 500 [Dwn] (5 cm) 500 [40 hrizntl] ( cm) ince nd d OT dd up t W, but DD up t the Equilibrnt rce ( W ), we will he t drw the Oppsite Weight Vectr. Weight (W ) 500 [Dwn] (5 cm) 900 [5 hrizntl] 7- ssignment: pg. 8 9 # t prighted b Gbriel Tng.Ed.,.c. Pge 5.

8 Unit 5: Vectrs pplied Mth 0 7-: Multipling Vectr b clr When multipling ectr (u ) b sclr (k), we simpl multipl the mgnitude f the ectr b the sclr. There re pssibilities with the directin f the resultnt ectr.. If k > 0, k u k u with the ME Directin s u.. If k < 0, k u k u with the OPPOITE Directin s u.. If k 0, k u 0 (O esultnt Vectr). Emple : Gien ectr, drw:. b. 6 cm 9 cm cm cm c. 0.5 d..5 e cm cm (Oppsite Directin) 6 cm (Oppsite Directin) cm cm cm Emple : Using the scle f cm 5, find the fllwing ectrs gien tht 0 [West]..5 0 [West] (4 cm) [West].5 50 [West] (0 cm) Pge 6. prighted b Gbriel Tng.Ed.,.c.

9 pplied Mth 0 Unit 5: Vectrs b. 0 [West] (4 cm) 0 [Est] 40 [Est] (8 cm) c [Est] 0 [West] (4 cm). 6 [Est] (5. cm) Emple : ind the lue f the sclr, k, gien the fllwing infrmtin.. 4 m/s [rth] nd k 4 m/s [rth] b. 9.8 m/s [Dwn] nd k m/s [Up] k( ) k k 4 m/s[rth] k k 4 m/s[rth] Units nd Directins must be the ME befre ncelltin. The sclr, k, is lws UITLE k( ) k k m/s [Dwn] m/s [Up] k 9.8 m/s [Up] 9.8 m/s [Up] Oppsite Vectrs is used t bring but the ME Directin. k 0.5 nlzing Vectr b its Hrizntl nd Verticl mpnents r n gien ectr, we cn frm ight ngle Tringle b tking the Vectr s HYPOTEUE. csα csα W α sinα sinα -is u u u u cs u u u cs u sin u u u sin E -is W w sin β w w wsin β w w β w w cs β w w wcs β -is p γ p p csγ p p pcsγ E -is p p sinγ p p psinγ prighted b Gbriel Tng.Ed.,.c. Pge 7.

10 Unit 5: Vectrs pplied Mth 0 Emple 4: ind the hrizntl nd erticl cmpnents f the fllwing ectrs. lcultr must be in DEGEE Mde!. 46 [0 W] b. 45 km/h [65 ] 46 (sin 70 ) W is E -is W -is km/h 5 45 km/h (cs 5 ) 85.8 km/h 79.6 km/h 45 km/h (sin 5 ) E -is c. d 85. m [57 E] d. 8. m/s [9 ] W -is d 85. m (cs ) 57 E -is d 85. m (sin ) W 8. m/s (sin 5 ) 8. m/s (cs 5 ) -is E -is 5 9 d 85. m d.06 m d m 5.7 m/s 6.8 m/s 8. m/s Emple 5: Gien u [rth], [Est], sclrs h nd k, nd w hu + k. r w 8 [ ], determine the lues f the sclrs h nd k. -is W k w 8 cs ( k 6.7 ) k 6.7 [Est] E -is k [Est] h u w 8 (sin ) k 6.7 w 8 h u 4.6 hu 4.6 [rth] h u [rth] h ssignment: pg. # t 5 Pge 8. prighted b Gbriel Tng.Ed.,.c.

11 pplied Mth 0 Unit 5: Vectrs 7-4: ling Vectr Prblems b mputtin sic Trignmetr eiew r n right ngle tringles, we cn use the simple trignmetric rtis. Oppsite b Hptenuse c djcent sin ppsite hptenuse cs djcent hptenuse tn ppsite djcent OH H TO e sure tht ur clcultr is set in DEGEE under the settings in ur MODE menu! - thet rible fr ngle pitl letter is lws used t lbel the ngle. The nme fr the side tht is ppsite t the ngle hs the crrespnding letter in smll cse. Emple : ind tn X, X nd XZ. X X 5 cm Lbel the sides nd ngle z 5 cm dj hp cm Y 8 cm Z Y 8 cm pp Z tn X tn X pp dj 8 5 tn X 8 5 X 8 nd T prighted b Gbriel Tng.Ed.,.c. Pge 9.

12 Unit 5: Vectrs pplied Mth 0 The ine Lw r n tringle, the Lw f ines llws us t sle the rest f the tringle if we knw the mesure f n ngle nd the length f its ppsite side, plus ne ther ngle r side. c b sin sin b sin c When using the ine Lw, we nl use rti f tw frctins t ne time. The sine Lw r n tringle, the Lw f sines llws us t sle the tringle if we knw the mesure f n ngle nd the length f its tw djcent sides (se ), r if we knw the lengths f ll three sides (se ). c b b + c ling fr cs : b + c bc bc bc( cs ) ( cs ) b + c cs b + c bc When gien the length fr ll three sides, sle fr the lrgest ngle first! This will eliminte n chnce fr n mbiguus situtin. ( cs ) ngles in Prllelgrm 80 In n prllelgrm, the Oppsite ngles lws he the ME mesure. The djcent ngles will lws DD up t Pge 0. prighted b Gbriel Tng.Ed.,.c.

13 pplied Mth 0 Unit 5: Vectrs Emple : In, 05, b 8 m nd c 5 m. le the tringle t the nerest degree nd t the nerest tenth f metre.? b 8 m 05 c 5 m b 8 + c + 5 bc ( cs ) ( )( 5)( cs05 ) m sin sin b sin05 sin ( sin05 ) sin 4.4 sin Emple : In prllelgrm D, 50, 80 cm nd 5 cm. ind the length f the dignl t the nerest tenth f centimetre. Determine t the nerest degree. D b c ? 80 cm bc ( cs ) ( 5)( 80)( cs0 ) 05.9 cm cm sin sin b sin0 sin ( sin0 ) sin 05.9 sin ? c 80 cm 0 b 5 cm prighted b Gbriel Tng.Ed.,.c. Pge.

14 Unit 5: Vectrs pplied Mth 0 ling Vectrs lgebricll. Drw Vectr Digrm with eerthing prperl lbeled.. r ectrs tht frm ight ngle Tringle, line up ectrs frm Hed t Til. Use the Pthgren Therem nd the Tngent ti t sle fr the Mgnitude f the esultnt Vectr nd its mpss ering r Heding.. r ectrs tht d OT frm ight ngle Tringle, use n ne f the tw methds belw. Prllelgrm Methd: (cn nl be use t dd TWO Vectrs). Line up ectrs frm Hed t Til b sliding the secnd ectr lng the first. b. mplete the remining side t frm Prllelgrm. c. Using the Lw f sine, find the Mgnitude f the esultnt Vectr. d. Using the Lw f ine, find the prper mpss Heding r ering f the esultnt Vectr. Vectr mpnents Methd: (cn be use t dd TWO r MOE Vectrs). ind the hrizntl nd erticl cmpnents f LL Vectrs. b. dd up ll the hrizntl ectrs (be creful with the signs). This is the esultnt Vectr s Hrizntl mpnent. c. dd up ll the erticl ectrs (be creful with the signs). This is the esultnt Vectr s Verticl mpnent. d. Using the hrizntl nd erticl cmpnents f the esultnt Vectr with the Pthgren Therem, determine the Mgnitude f the esultnt Vectr. e. Using the Tngent ti, find the prper mpss Heding r ering f the esultnt Vectr. Emple 4: ferr is crssing chnnel 50 km wide with elcit f km/h [rth]. The chnnel hs current tht is 8 km/h [West]. Wht wuld be the mgnitude nd directin f the ferr s resultnt elcit? 8 km/h [W] hnnel 50 km err s Velcit km/h []? km/h [] urrent 8 km/h [W] km/h tn 8 4 km/h [4 W] r 46 Pge. prighted b Gbriel Tng.Ed.,.c.

15 pplied Mth 0 Unit 5: Vectrs Emple 5: 50 [5 ] + 85 [40 ] Prllelgrm Methd lide ectrs lng ech ther until the ectrs re lined up rm HED t TIL t frm prllelgrm Tking the Tp Tringle nd ppl the sine Lw nd ine Lw c b 85 b 50 + c bc ( cs ) ( 50)( 85)( cs 75 ) sin sin b sin75 sin ( sin75 ) sin 4. sin [55 E] r [55 ] prighted b Gbriel Tng.Ed.,.c. Pge.

16 Unit 5: Vectrs pplied Mth 0 Emple 6: 45 m/s [45 ] 6 m/s [ ] Vectr mpnents Methd 6 m/s [ ] 45 m/s [45 ] 6 m/s [ ] 45 m/s [45 ] + ( 6 m/s [ ]) 45 m/s [45 ] + 6 m/s [ ] 6 m/s m/s Obtin the Verticl nd Hrizntl mpnents f ech ectr we re but t dd m/s 6 m/s (sin 57 ) 45 m/s (sin 75 ) m/s m/s 6 m/s [ ] m/s (cs 75 ).647 m/s 6 m/s (cs 57 ).768 m/s m/s m/s. m/s 98.0 m/s m/s m/s m/s m/s tn tn m/s m/s 98.0 m/s [E77 ] r [ E] r [ ] Pge 4. prighted b Gbriel Tng.Ed.,.c.

17 pplied Mth 0 Unit 5: Vectrs Emple 7: plne is fling t 00 feet with cruising speed f 600 km/h heding 55 E. If the elcit f the wind is 50 km/h frm the west, determine the mgnitude nd the directin f the ircrft s resultnt elcit W 50 km/h 55 5 E W Using the Prllelgrm Methd 50 km/h E 600 km/h 600 km/h 600 km/h Tking the Tp Tringle nd ppl the sine Lw nd ine Lw. 50 km/h b 50 km/h 45 c 600 km/h b 50 + c bc ( cs ) ( )( 600)( cs45 ) km/h W 50 km/h km/h E 78 km/h sin sin c sin45 sin ( sin45 ) sin 78 sin km/h [8 ] r [E8 ] r [6 E] prighted b Gbriel Tng.Ed.,.c. Pge 5.

18 Unit 5: Vectrs pplied Mth 0 Emple 8: wden sign with weight f 400 is hung frm the ledge f building b tw rpes. One rpe pulls t 0 t the hrizntl frm the left, nd the ther pulls t 4 t the hrizntl frm the right s illustrted n the digrm belw. Wht re the mgnitudes f the tensin frces eerted b the tw rpes? 0 4 The tw rpes eert cmbined tensin frce equl t the ppsite ectr f the sign s weight. Wden ign Using the Prllelgrm Methd 400 (up) ?? ? Hrizntl? ? 400 (dwn) Hrizntl Tking the Left Tringle nd ppl the ine Lw. c sin sin b sin 7 sin b 400 sin 48 b ( ) ( sin 7 ) sin sin c sin 7 sin c 400 sin 60 c ( ) ( sin 7 ) b 60 b.6 c ssignment: pg. 8 9 # t EDO: pg. 8 9 # t 0 (withut using scle digrms) Pge 6. prighted b Gbriel Tng.Ed.,.c.

19 pplied Mth 0 Unit 5: Vectrs Vectr Prject: Vehicle llisin nlsis Purpse: T recnstruct ccident detils using the lw f cnsertin f mmentum. ckgrund Infrmtin: Mmentum: - ectr quntit which is the prduct f n bject s mss (kg) nd elcit (m/s r km/h) Mmentum Mss Velcit p m Emple: lculte the mmentum f 500 kg cr is ming 0 W t 60 km/h. p m (500 kg)(60 km/h) p 0000 kg km/h [0 W] nsertin f Mmentum: - when bjects cllide, the ttl mmentum befre the cllisin is the sme s the ttl mmentum fter the cllisin. Ttl Initil Mmentum Ttl inl Mmentum p i p f If tw ehicles cllided t right ngle, nd the ehicles gt TUK TOGETHE fter the llisin, the ectr digrm wuld be s shwn belw. p i p f Vehicle with mss (m ) nd elcit ( ) Vehicles nd with Ttl Mss (m + m ) nd inl Velcit ( ) f m + m (m + m ) f Vehicle with mss (m ) nd elcit ( ) knwing the ngle fter the cllisin, the msses f the tw ehicles, nd their finl elcit (usull b mesuring the length f the skid mrk), we cn find ut their elcities befre the cllisin. prighted b Gbriel Tng.Ed.,.c. Pge 7.

20 Unit 5: Vectrs pplied Mth 0 If tw ehicles cllided t right ngle, nd the ehicles EMI EPTED fter the llisin, the ectr digrm wuld be s shwn belw. Vehicle with mss (m ) nd finl elcit ( ) f Vehicle with mss (m ) nd elcit ( ) Vehicle with mss (m ) nd finl elcit ( ) f p i p f m + m m f + m f Vehicle with mss (m ) nd elcit ( ) knwing the ngles f bth crs fter the cllisin, the msses f the tw ehicles, nd their finl elcities (usull b mesuring the length f the skid mrk), we cn find ut their elcities befre the cllisin. Prcedure: Prt : llisin f Tw Vehicles tht gt TUK TOGETHE fterwrds. Tw ehicles cllided t n uncntrlled intersectin. Vehicle ws treling estbund nd Vehicle ws treling nrthbund. ne knew hw fst the were ging but bth ehicles gt stuck tgether treling t (sme ngle) E directin fter the cllisin. Eentull the stpped nd left skid mrk.. p nd fill ut the fllwing tble. Pick numbers fr the lues frm the brckets belw. Mss f Vehicle (500 kg t 000 kg) Mss f Vehicle (500 kg t 000 kg) ngle bth ehicles mde fter the cllisin (5 E t 75 E) Velcit f bth ehicles fter the cllisin (40 km/h t 0 km/h). Drw ectr digrm with the pprprite ectrs nd prper lbeling. The digrm shuld be drwn t scle nd the scle fctr lbeled. 4. ind the elcities f bth ehicles just befre the cllisin using:. ur scle drwing. b. the lgebric methd. Pge 8. prighted b Gbriel Tng.Ed.,.c.

21 pplied Mth 0 Unit 5: Vectrs Prt : llisin f Tw Vehicles tht EMI EPTED fterwrds. Tw ehicles cllided t n uncntrlled intersectin. Vehicle ws treling westbund nd Vehicle D ws treling suthbund. ne knew hw fst the were ging. fter the cllisin, bth ehicles were treling t different (sme ngle) W directins fter the cllisin. Eentull the stpped nd left tw different skid mrks.. p nd fill ut the fllwing tble. Pick numbers fr the lues frm the brckets belw. Mss f Vehicle (500 kg t 000 kg) Mss f Vehicle D (500 kg t 000 kg) ngle Vehicle mde fter the cllisin (0 W t 44 W) ngle Vehicle D mde fter the cllisin (46 W t 80 W) Velcit f Vehicle fter the cllisin (40 km/h t 0 km/h) Velcit f Vehicle D fter the cllisin (40 km/h t 0 km/h). Drw ectr digrm with the pprprite ectrs nd prper lbeling. The digrm shuld be drwn t scle nd the scle fctr lbeled. (Yu might he t drw mre thn ne digrm fr this prt.) 4. ind the elcities f bth ehicles just befre the cllisin using:. ur scle drwing. b. the lgebric methd (either b prllelgrm methd r ectr cmpnents methd). te:. ll digrms drwn must be t scle nd prperl lbel.. ll wrk nd clcultins must be shwn clerl.. tudents cn wrk tgether t discuss the prject, but the shuld ech he their wn numbers t wrk with nd d their wn clcultins. tudents wh cpied frm ech ther will end up shring the mrk. Let s s the mrk ws 70% nd tw students were inled in cping ech ther s wrk. The ech get 5%. 4. Lte Prject hnded in ne d fter the due dte is cunted s 0% ff the ttl mrk. Prject hnded in tw ds nd lter will nt be mrked. Due Dte: prighted b Gbriel Tng.Ed.,.c. Pge 9.

22 Unit 5: Vectrs pplied Mth 0 7-5: Vectr Prblems in -Dimensins When nswering ectr prblems in -dimensins, it is helpful t mke b t shw ll the ngles inled. UP W (int the pge) E z (ut f the pge) DOW α c c z hs the directin f Est () rth nd α s the ngle f Eletin. LL Tringles in the b re ight ngle Tringles! The dignl f the b ( ) cn be fund b the -Dimensinl Pthgren Therem, + + z + + z O nd c + c + z The ngles nd α cn be determined b using the Tngent ti. tn sinα z Pge 0. prighted b Gbriel Tng.Ed.,.c.

23 pplied Mth 0 Unit 5: Vectrs Emple : crne is lifting up wll with frce f 500. One wrker pulls it with 600 f frce twrds the nrth nd nther wrker pulls it 500 twrds the west. Wht is the resultnt frce n the wll? Up? tn sinα rth 50 α West c α [W50 ] with n ngle f Eletin f 6.5 Emple : tennis bll hs weight f 50 nd is thrwn up during sere with n pplied frce f 80. If the wind eerts frce f 5 twrds est, nd the pler s rcket hit the bll twrds the nrth with frce f 700, wht is the resultnt frce n the bll? pplied rce 80 [Up] Weight 50 [Dwn]? et Verticl rce 0 [Up] Up α c 700 rth tn sinα α Est 7.8 [E87 ] with n ngle f Eletin f 0.5 prighted b Gbriel Tng.Ed.,.c. Pge.

24 Unit 5: Vectrs pplied Mth 0 Emple : plne is tking ff with speed f 400 km/h twrds the suth nd climbs t n ngle f with the hrizntl. sted wind is blwing frm the west t 60 km/h. Determine the speed f the plne reltie t the grund, nd the ngles the plne s trck mke with the hrizntl nd the grund. esultnt peed (reltie t the grund) α ngle the Trck f the Plne mkes with the Grund ngle the Trck f the Plne mkes with the Hrizntl Up? α? 400 km/h? c uth 60 km/h Est tn tn 400 km/h ( 400) tn km/h km/h 60 km/h tn km/h sinα tnα km/h 4.6 km/h α ssignment: pg. 6 7 # t 8 Pge. prighted b Gbriel Tng.Ed.,.c.