# Chapter 4 2D and 3D Motion

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1 Chpe 4 D nd 3D Moon I. Defnon II. Poecle oon III. Unfo ccul oon IV. Non-unfo ccul oon V. Rele oon

2 Poon eco: eend fo he on of coodne e o he pcle. 4. k z 4. k z z I. Defnon Aee eloc: 4.3 k z Dplceen eco: epeen pcle poon chne dun cen e nel.

3 Innneou eloc: d zk d d d d d dz d k 4.4 -The decon of he nnneou eloc of pcle lw nen o he pcle ph he pcle poon Aee cceleon: 4.5 Innneou cceleon: z k d d d d d d d d z k 4.6

4 II. Poecle oon Moon of pcle lunched wh nl eloc, nd fee fll cceleon. The hozonl nd ecl oon e ndependen fo ech ohe. - Hozonl oon: = = = conn co 4.7 Rne R: hozonl dnce eled b poecle befoe eunn o lunch heh. - Vecl oon: = - = conn n 4.8 n 4.9 n 4.

5 - Teco: poecle ph. 4. co n co co n co Hozonl ne: R = - ; - =. 4. n co n co n co co n n co co R R R R R R R Mu fo lunch nle of 45º Oell upon: he houh whch he poecle oe h no effec on oon fcon neleced.

6 : A hd ben whe o how o f be, 7 fee dn. H be hown peed 85 h. If he how he bll hozonll 3 f boe he ound, how f fo f be wll h he ound? b Fo he e nl heh, wh upwd nle u he hd ben how he bll f he f ben o cch 3 f boe he ound? c Wh wll be he e of flh n h ce? h=3f B3 B B =38.7 h h foo 3 fee.9 h=3f Hozonl oeen Vecl oeen fo B B3 θ B The bll wll h ound.3 fo B 4.9 n co 38co n n co 38co n n 4.9

7 N7: In Glleo Two New Scence, he uho e h fo eleon nle of poecon whch eceed o fll ho of 45º b equl oun, he ne e equl Poe h een. θ=45º =R=R? n b n cob co n b n b n cob co n b R R' n 9 R R' n n co co9 h Rne : R n d 45 n9 45 n9 n n 9 co co9 n co co

8 III. Unfo ccul oon Moon ound ccle conn peed T n co n n n co n co co n p p p p du lon deced d d d d d d - Peod of eoluon: - Acceleon: cenpel -Veloc: nen o ccle n he decon of oon. Mnude of eloc nd cceleon conn. Decon e connuoul.

9 54. A c de e-o-ound whle unn wh unfo ccul oon. A e =, he c eloc : = 3+4, eued on n hozonl coodne e. A e =5 eloc : = Wh e he nude of he c cenpel cceleon nd b he c ee cceleon dun he e nel -? In 3 he eloc eeed he c eche he oppoe de of he ccle T c

10 IV. Non-Unfo ccul oon - A pcle oe wh n peed n ccul ph. - The cceleon h wo coponen: - Rdl =- c =- - Tnenl = dd - cue he chne n he peed of he pcle. d d - In unfo ccul oon, = conn = =

11 V. Rele oon Pcle eloc depend on efeence fe PA PB BA 4.5 D Fe oe conn eloc d d d d PA PB BA PA PB d d 4.6 Obee on dffeen fe of efeence eue he e cceleon fo on pcle f he ele eloc conn.

12 .5 flh flh lunch lnd flh b lunch lnd el, 75. A led oe n he nee decon peed whlebllofcehofoheledwheloc = + ele o he led. When he bll lnd, hozonl dplceen b ele o he ound fo lunch poon o lndn poon eued. The fue e b funcon of. Aue lnd ppoel lunch heh. Wh e he lue of nd b? The bll dplceen b ele o he led cn lo be eued. Aue h he led eloc no chned when he bll ho. Wh b when c 5 nd d 5? Lunch eloc ele o ound Dplceen ele o ound b flh flh.5 b b = + b b flh Dplceen ele o he led Rele o he led, he dplceen doe no depend on he led peed Anwe c= Anwe d flh b 4 4

13 A do whe o co e o pon decl oppoe hown. I cn w n ll we nd he e flown. A wh nle wh epec o he lne onn he n nd fnhn pon hould wn? fnh f θ f n co n 3 n co f co f f 3

14 A pcle oe wh conn peed ound he ccle below. When pon A coodne e =, =3 nd eloc 5. Wh e eloc nd cceleon pon B? Epe ou nwe n e of un eco. B B 5 B B A 8.3 A 5

15 . A hn lde 7.5 boe ound leel wh eloc of 8 n nle of 3º below he hozonl nd conn cceleon of, up. Aue = he nn u decbed nd we n equon fo he eleon of he hn lde funcon of, wh = ound leel. b Ue he equon o deene he lue of when =. c Epln wh hee e wo oluon o p B. Whch one epeen he e ke he hn lde o ech ound leel? d how f doe he hn lde el hozonll dun he nel beween = nd he e eche he ound? Fo he e nl poon nd eloc, wh conn cceleon wll cue he hn lde o ech ound leel wh zeo eloc? Epe ou nwe n e of un eco , 3 h=7.5 3º = 8 8co 3 o 8n If he ound w no old, he lde would woop down, pn houh he ufce, hen bck up n, wh he wo e of pn ben =3, =5. d Vecl oeen : f f f Hozonl oeen :

16 4. A bll o be ho fo leel ound wh cen peed. The fue below how he ne R wll he eu he lunch nle θ whch cn be lunched. The choce of θ deene he flh e; le epeen he u flh e. Wh he le peed he bll wll he dun flh f θ choen uch h he flh e.5? R flh.5 n 4.9 n n n n.5 n.5 3 θ The lowe peed occu he op of he eco hlf of ol e of flh, when he eloc h pl n -coponen. n hlf eco co3 fo. 5 Gph R 4 fo 45 R n n 4 n co

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