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RELATIVE VELOcTTY~ * AQt 2 boolgs A & rovers und Ce tavight Care. snl OF Ky & x, she crs pl of the body fare the an a fee hime. 50 the asp. oF the toaly & with reespocd ra Yo 2 VP OBA B Ay oD : yitoe £0 Line 1 Differentiate / Derivative eq? () with reas) Xen Ake © xy olf ad At 7 Vo = Vis-— Va . Wyherte Vb, = Volocity of Butt reospect oA. . te, the relive velocity of @& axth reospet AL. Dt = 23/11/202) Vp = Original Veloctty of body B. i és wotet = ttl Velocity of B weth Freepers to greeurel a rps Vy = Original Velocity of body A. . 6 y = ‘eet of 4 with reaspect do (en ap Vag: Vere . ; tet. B So, relative velocity of A Wet, Be, b., ete V-Ve ay? = Flo Vap ~ 4 B “ng, « Ya-Me B A Ted a Cele “5 oa Ey 4 ‘ Lecemeg) é 9 f 20m }5 i tome fia op Sep terens ow bet te coeknel we) ten iicey) Me Nol. VW Ven = Va Va = Vad Vb, BA 4 = 07 20 ~ 20°10 - -loms! = [Om/s he C Scanned with OKEN Scanner 2 Tp mis —— 2omis (0 +30 = Yome . ) Vig = ee Ts VRAMEE ORM ULAT vie aw Vur= Vato~ Vee, Vp = tebe Vang Veg 2 Wily ary 7 2 = Ving 20 : ; a =» Y =22mis. = germs - 15 m/s 7/6 2 Mme —» Viey= — ® Von ~ Vas = 22-F _ to an 1 C Scanned with OKEN Scanner VET APLAR §- A treatn moves with a speecl of 30 kth 99 the 19? 15 Minttes With another speed of 40 kmh the next 15 minutes + And “thon with a speed of 60 Km/h 7 the las? Bb rinutes . Aleulate the avg speel of taatn fore dis journoy , oles The tat moves @© cvltha spetd of a0 v= sokralh « feme t, = 15min = Gh. ~ Speed Vg = YOkm{h time ty = Io min = ih. spech Tote GORD vm tye B20 Mn .= zh. Avg. Speocl > Sit Sais | Boxy KETO tooxE rs 7 H+ tt [v= . a3 tyly dt 52 VE wIY TQ - 30,409,120 . Ta ek ee az - 4F FO #30 oe VER km 2 The. posetion of an object moving: along x-axis is given by X= atbt® whore Q= 8.5m. & b= 2.5m/s* ¢ = mogusured 27) second- What zs The velocity at f=0 soc & t= 2 sc 7 hihat is the avg. velocty “het? t = asec Bd= Ysec ? ae : it F an object X= at bt sss ; Rosina? ‘ = 85 2642 p AKL Alastety Velo cat V old ~ cl ( 85-549). At — be aedvaen, of Aexee is ne Nie = ot C Scanned with OKEN Scanner = O mis. Yew . Upz9 2 XAS*Q> [OM)s. . Xp -% Pp- Aa Vawg = — 2 Ale6b-a-—Yb , Pe. bbe I8mJs. ROU . Y-2 A 3- The dtsplacemant Cin m) of a particle movers cong, Ken's lo given by x= 18+ +5t®. Calculate (ty) Tho instantaneous velocity at t> 2 see . (fr) AVS. velocity bot? ta 250c. & 425sec. (iil) Breten-ronces al? fins thy = OlXast gf (5t>Het — Velocity Gee +, dst te) = Stet dist | “alt . = Sat, wat ar ar QGE TIS FOF EE at t= QSec =BSXQ +13 = 98 MIs, \! ro) Vinstantencouc WD Vag 2 Oe 18X34 S¥3"~ lena eae "4 ty tg’ geo = 43 MIs - (iy acel"= dv, d Corie) d4 ap _ lt + 18d a+ ol4— > 10 40 C Scanned with OKEN Scanner Bribe = PROJECTILE MOTION "A projectile 36 a mame given Jo a body which Thrown 2a Space wih some enptial velocite \ then celled to meve. Under tre acton of glivity ctlone wethouk beg pred — pelled by any Lyire Or eases fuel Ext. 4 fave lien thrown by an atholore © A ballet fred trom @ gun « A bat) thrown by 1% plouyer ' * Projectile Fereed at an angle © weth horizontal > Y a ‘ oh Ucose BY te £50 # Consider a body thrown into space by making an angle . O wrth horizontal + ; 4a = veloc! fy OF the body - ® U) = rested: tanto 2 CoMmpo Nerch Thais » UCO6@R using as horizontal conponent oll vereboal component roespode yy . romain consta a a The. harcixon tal component Cucos@) nN constant threo egh- out 2 mokon K Pre vorcticat Component (UsIne) charge, wih Ferre urder the effect OF Oramity. . thes componant 4° clecreecises , becomes zero at the higte 9~ , point Me exter which if nee PIVCKLASES fl tho - prjactie heals TM Qh x | * | C Scanned with OKEN Scanner fg" of raj ectory > - (Leng) » This 16 the eg” fhat gives édea about Mme nah Pollowecl- by te projectere . ; ) « Let at an inctant C4) 1 the sy v6 el pein? rn - So the horizontat distance covered vy the Podginkime t Me UjlCOse® xt 7, = a? ca . at UlOSe » Por verckccul distance’ coveriaal 8 abt pat? = =usino ~ by there inemet Soy Y= using t- + xP? a 7 SPE ices” XO ea q = ax ba Whee Q= taAn® b= 2utos’® Eq! wy represenss ey” of a parate's Se path followed by the projectdle fs parwiolee . . Fema of Flight ° - © Oh) tho dime ako) by the pro) pectle Seon a the iPspartt pe Po projected fell 7t reeaches a point mm the Aorixontal plane 5 : (as C Scanned with OKEN Scanner Moximun) Hetaind fh max). gt (6 the maximum listince upvered by the prenjec tile in syertica lire”, ; we knod + Veu'= 2a6 ' Fore verctrcat motcan v= 0 yp aed “= USING , 5 = hmar )_O- U*sin’® = 29% hingx I? hamax L welt war Bin?O | shan J. Horizontal Kange : + (®) | 175 the horizonte) CHstinte ~covened "f tre preoctile cueing tho time OF Aight . » Horizontal rege range = Hortzon etl velocity x me of Mighh. : ye re | 7] R= Uc0s@ xX Busine [- vane Do VE SR Condition fore Miaximum We know that, R= ae R will be mari rue when Sin 2e@ = 1 A Sin 2 = SnUP 7 RE 20 ~ 4rq0° > O= 45 ¥ re bod wry ll coverc fn a xara. ny horizon al range thoy do ey making angle 45° with horizontal + omaxontal Range > C Scanned with OKEN Scanner Question ae ; 1) 4 Dealy >s thrown vertically upwucttcd wrth vere My of 96 m/s. Colcetatdep (ty Time of aseonr 1D) fy (ir) 3 peel on reach fhe qrouinck ; ) Teme Of ascent Ta> using d 9.8 m/5™ . = 2S, cD) Teme of cle scent ty = musing . 26. (i) EVO V ey = 2as hefee $. OF uu =/9.6 veut 0 qv dase a Ve u IV 19.6 m/s - 78 True so ¢r ls iy. Ve - a Om eel On) ran jhe ground F iS. -19- emis 2 A ball thrown Up ry a player 15 cag hoy DAW nS 45 after the Areata UE Cie oe kde? fhe ball wae” “throw? L (i) Whore was the bat the stare * t Ae. seme of Pght rye fhe: Ben ag thrown , inital ~velocily =U time of w 5 phon dng ball w Fino ~elocita * 6 ascon@ t22. ator) [-Ssec. () 3 sec ater - > Is? Ve ana > 0 = Ure9.B)x 4) 2 +| A mee 2 7 - ud rt ape~ Binerd t 1x (4.8) 94 thy Height i. 16h ~ ‘ / C Scanned with OKEN Scanner For vertical motion us 0 Ps is es _ RES 74> Kar where be oa a tS og reepresends ay? ny a mabola (30, hea parr Followed by the preiet: 5 pons Teme OF Pltght > Qt = is tne total emne fore which ane mp feemains wits Flight . for ¢ be tho teme oF He, $0 fr vertcal cleorntd ated eh Se wt tZat? : Be ott ag ty da Horizontal Range PIMs Gipsy ‘TR fs the horizontal aistante covered ca te projectile. caning. its time of Plegtet . Horizontal distance = Hordzcontal elec Timo Pliglit 7) R= Ute an C Scanned with OKEN Scanner orncah> jommaricas yA cretcket batl #6 dhicown a. L Space, of aein/e 0.0 A cine “A0° akove the hererzontcul . Cocleulere >. (Maximum height _ (i) Teme faken by Ne fall fo riotuch the sore lave (ii) The horizontal cistunce Yreom tno throwerc to the point Where the Path refeuns to, the some tlorel | nse Thiteal velocity Us 28 ms —_—— — oO = 20 t=. 4: 2 mys (0 Maxime height hw _ —ubsind AT “. ee Sin30” mn*/5% : 8616 QRS [ek 20 Peale] : Lay toe STRET , =... lom. () Gime taken by ball 1 rokuny fo the same “towel ° Ruse 2 BERS OB RE Tp = oa GT a A 4.8. phe” = 2. BES. 7 ay - kane. 28 x Sin60xM 1” (Horizontal stance ~% 4.8 m/s = By x2 — 2 TONES Mm: exe as a Lo C Scanned with OKEN Scanner & A projectéle has O range o7. som & rewaches Q maxinury faint OF tom. Catewlate ne angle al wich gro pritictle 74 Ered P . And: Gtven, Tee range R= 50M. ~ ‘Amax = 107. Re u®sin26. co m, >) u'2108.0050 > Som JR ; Sy Dax = u°sina 2 A) — (a) BAND, ASHES, Be HEU wote= 2 2 2) E 7 6 = OO sy, E >) 6 = tan (2) C Scanned with OKEN Scanner 7 Db MH /12 1202 \ wales. MF the _peojectile at any tnslavt Horizontal velodig ; ot Voe= Unt at Vy = us. Verizcal vee Vy = Uy Tey Vy = @ * y= Oorgt=¢ | Resultant velocity » ven = tg <1 £ ; ape ton(®) : Ak tho any instant 't, ket the velocity of ‘the pregeck le. be va Tho. velocity ‘v’ has “2 rectangular Components : (1) Horeizontat component of welocliy Vg = Cat ge . ad Va = ha © Ci) Vertical component of velecita Wye Uyt ayt i eek tat Ty 2 4t 2 “The resultant velocity at he point?’ = ve ery TY the velocity VV makes an angle Pp with the hordexentel v b Hon ! tanp > ts ue @ Ve ay p* tar! ( 9) # C Scanned with OKEN Scanner 
