Ex: An object is released from rest. Find the proportion of its displacements during the first and second seconds. y. g= 9.8 m/s 2
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1 FREELY FALLING OBJECTS Free fall Acceleraion If e only force on an objec is is wei, e objec is said o be freely fallin, reardless of e direcion of moion. All freely fallin objecs (eay or li) ae e same acceleraion downward, due o raiy. In problem solin we enerally ake = m /s for simpliciy. Downward = = = m/s =s =3s = =s =3s Upward = = m/s Problem solin sraey: ) Firs coose (+) and (-) direcions. Generally direcion of iniial elociy is aken as plus. ) Coose zero leel 3) We can use all e old formulas, only replacin a by. = =9.8 m/s =9.6 m/s =9.4 m/s = m/s =3 m/s A sone is dropped is dropped from m aboe e round. Find is elociy and ei 3 s laer. = Noe: does no ie e ei, i ies e displacemen =3s =s = = + = +/ =( - )/ m = 9.8 m/s = m/s =3 m/s =? An objec is dropped from e op of a buildin m i. a) Wen does e objec srike e round? b) Wa is e final speed? Ex 3: An objec released from res from i aboe e round reaces e round wi 35 m/s speed. Find iniial ei of e objec. =? = m/s Seba Kyryz Turkis Hi Scools A ball is rown direcly downward wi an iniial elociy of 8 m/s from a ei of 3 m. a) Wi wa elociy does e ball srike e round? b) Wen does i srike e round? An objec is released from res. Find e proporion of is displacemens durin e firs and second seconds. =? Ans: Take = as e sarin poin: since = =/ a : =/ a = + =/a () =4; so =3 {Te answer is 3. Now, if we wan, we can speak abou e =s :3:5:7 proporion of e displacemens of an objec for eac second wen released from res} (HW ) Find e proporion of elociies. =? An objec is rown upwards wi an iniial elociy of m/s. Find is elociy a) One second laer b) Tree seconds laer Sol: [Firs draw e picure; coose direcions on e picure. We enerally ake direcion of as plus.] Vecor formula: = + [Now pu e alues ino formula by lookin a e picure o decide abou e sins.] Scalar equaion: =(+) + (-). = + m/s =(+) + (-).3 = - m/s = =s = = Noe: If a alue is ien in e quesion ake i as (+) or (-) by lookin a e picure. = + - 4
2 If a alue is no ien (or i is waned) in e quesion ake i as plus; if i is minus e formula will find i as minus a e end. An objec is rown upwards wi an iniial elociy of m/s. Find is posiion a) One second laer b) Tree seconds laer {Draw e picure afer calculaion} Noe: Te formula finds e displacemen, no e disance. Noe: We don use wo formulas for oin up and down, because e acceleraion does no cane alon e wole moion. An objec is rown upwards wi an iniial elociy of 3 m/s. In wa ei does is elociy decrease o 5 m/s? An objec is rown upwards wi an iniial elociy of 3 m/s. a) In wa ei does is elociy decrease o zero? b) Wa is e maximum ei of e objec? Find a eneral formula for e maximum ei and ime of fli. {Derie e formula: Ask: Wy is e elociy zero a e ies poin?; Answer: Because if i was no zero, e objec would o ier and is poin would no be e ies Ten pu f = in e formula =( - )/} max = up = down = max Seba Kyryz Turkis Hi Scools A ball rown erically upward is cau by e rower afer 8 s. Find a) e iniial elociy of e ball b) e maximum ei i reaces An objec is rown upwards wi = 5 m/s. Find is displacemen afer 5 s. Find =? f f =? f {Draw e picure} A balloon is m oer e round oin up wi 5 m/s wen a passener releases a sone. Find e ei of e sone (aboe e round) 4s laer. A boy rows is faer s walle upwards from 5 floor window wic is m aboe e round. Find iniial elociy of e walle if i srikes e round 3 s laer. A suden rows is keys erically upwards o is friend in a window 4 m aboe. Te keys are cau.4 s laer by is friend. Find elociy of e keys: a) wen ey are rown b) wen ey are cau An objec released from res falls on o e round in 4 s. Wa disance does i rael in e las second of is fli? A fallin objec raels e las 8 m of is fli in s. From wa ei was i released? f fli = up = Noe: Unlike e ones before, ese formulas are no ecor formulas. You don worry abou direcion. Tree objecs are rown upward wi = m/s, = m/s, =3 m/s. Draw eir maximum eis. = MOTION IN TWO DIMENSIONS [ r y x = =45m Te ecor formulas = +a and r= =/a can be wrien seperaely for x and y componens of e ecors. Bu accordin o e fiure a x =; a y =; Terefore e formulas become: =m/s = =5m = m/s =m =3m/s Horizonal Verical x=x =y +/ x =x y =y + ] up =s up =s up =3s
3 Wrie e elociy and displacemen formulas for an objec rown wi in orizonal direcion. x= +/a x =y +/ x = (a x =) y = y + Wic means: x y x x = Find s=? if e bomb is o fall on o e sip. m Find elociy and displacemen formulas for an objec rown a an anle from e orizonal. y x 5 m/s s=? x Velociy: x =x (a x =) y =y + 5 m/s y x (Vecor formulas) y {Ineracie pysics demo} Te objec is rown in orizonal direcion wi =4 m/s.find e speed of e objec 3 s laer. =4 m/s =? Find e displacemen of e objec in 3 s. =4 m/s y Seba Kyryz Turkis Hi Scools Displacemen x=x =y +/ Wic means: = Terefore: y max = y x (Vecor formulas) = x = fli up = y =? By ow many meers does e orizonally so bulle miss e are 8 m away, if is muzzle elociy is 4 m/s? 8m =4 m/s =? A projecile is fired a an anle 53 aboe e orizonal wi 5 m/s iniial elociy. a) Find is maximum ei b) Find posiion and elociy 6 s laer. =5 m/s =53 =? = m/s =? =37 64 m A wa ei does e projecile i e wall? 3
4 =5 m/s m/s =? =45 m a) Wa is e iniial elociy of e projecile accordin o e fiure? b) Find e ime of fli =4m 5 m/s s=? =? = m/s =37 R=? Find maximum ei and maximum rane of e projecile in e fiure. =? =? =8 m R=48 m Find iniial elociy and sooin anle. A wa anle sould we row an objec for maximum orizonal rane? x y rane= x max =x fli = x y / = rane=( Cos) ( Sin)/ rane= (Sin Cos)/ = Sin Terefore rane is maximum wen Sin=; =45 Seba Kyryz Turkis Hi Scools An objec is rown in orizonal direcion wi 5 m/s from a balloon oin up wi m/s wen e balloon is 4 m aboe e round. Find s=? Sol: {Te ime formula ies a quadraic equaion so le s use e imeless formula} Relaie moion [We will inesiae relaie moion in wo pars: resulan and relaie moion]. Resulan elociy V AB is e elociy of A wi respec o (as seen from) B. Wa is e BC =4 m/s elociy of e boy wi respec o round? BG =? BC : elociy of boy wi respec o car CG : Velociy of car wi respec o round Wa is e elociy of e boy wi respec o round? BG =? Ans: BG = 6 + (-4)=m/s BC =4 m/s CG =6 m/s CG =6 m/s Also: R =R wen + =9 [Because Sin6=Sin ] 6 3 Wic one will fly ier? Wic one will o farer? Terefore: = + (ecor sum) AC AB BC Te boa is edin direcly WG =6 m/s across e rier. Wa is e elociy of e boa as seen by an obserer on e round? BW =8 m/s [You can ink of waer as a moin lon piece of paper, and e boa is a bu walkin on e paper.te bu will moe on e paper irrespecie of e paper s moion] 4
5 s =? W =3 m/s d = 4 m BW =4 m/s Maximum elociy of a boa in sill waer is =5m/s. Tis boa ses off d = 5 m W =3 m/s from one side of a rier 5m in wid, and raels direcly across e rier.find e passae ime for e rier if e speed of waer is 4 m/s.. Relaie moion Wa is e elociy of e car wi respec o (as seen by) e boy? boy =3 m/s car =5 m/s Terefore: Wa is e elociy of car A wi respec o car B? relaie = objec A =7 km/ Two sips are moin on e sea as in fiure. Wa is e elociy of small sip accordin o e bi sip? Find bo maniude and sirecion of relaie elociy. A obserer wes eas Vecor subsrucion B = km/ 3 km/ B 4 km/ Seba Kyryz Turkis Hi Scools 5
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