Projectile Motion CHAPTER 1

Transcription

1 CHAPTER 1 PHYSICS ESSENTIALS STAGE 2 Projectile Motion Subject Outline In the bsence of ir resistnce nd moing under the ction of constnt grittionl force, projectile hs constnt ccelertion in the direction of the force. The horizontl component of elocit of such projectile is constnt, nd the erticl component chnges t constnt rte. The time of flight nd the rnge of the projectile re clculted, nd the effect of ir resistnce on the motion is treted qulittiel. These ke ides re pplied to projectiles in sport (e.g. Ke Ides Students should know nd understnd the following Verticl nd Horizontl Components of Velocit 1.1 For projectile, in the bsence of ir resistnce, the: horizontl component of elocit is constnt; ccelertion is in the erticl direction nd is the sme s tht of erticll free-flling object. 1.2 The horizontl motion nd the erticl motion re independent of ech other: the constnt erticl ccelertion is independent of the horizontl speed. 1.3 The ccelertion of projectile, in the bsence of ir resistnce, is in the direction of the grittionl force. Determintion of the Verticl Component of Velocit 2.1 The equtions for constnt ccelertion in one dimension cn be used to clculte the erticl component of elocit of projectile t n instnt. Resolution of Velocit into Components 3.1 Velocit cn be resoled into its horizontl nd erticl components t n instnt. Time of Flight 4.1 The time of flight of projectile is determined b the chnge in the erticl component of elocit nd the ccelertion. Rnge 5.1 The rnge of projectile is clculted b multipling the horizontl component of elocit nd the time of flight. Mximum Height 6.1 The mximum height of projectile cn be clculted from the erticl component of the initil elocit nd the ccelertion or the time of flight nd the ccelertion. Effect of Air Resistnce 7.1 Air resistnce cts in the opposite direction to the elocit of projectile t n instnt. Intended Student Outcomes Students should be ble to do the following 1.1 Gien multi-imge photogrph of projectile, demonstrte tht the: horizontl component of elocit is constnt; ccelertion is in the erticl direction nd is the sme s tht of erticll free-flling object. 1.2 Drw ector digrm in which the horizontl nd erticl components of elocit re dded, giing the resultnt elocit ector t n instnt. 1.3 Using trigonometric clcultions or scle digrm, clculte, from its horizontl nd erticl components, the mgnitude nd direction of elocit ector t n instnt. 1.4 On digrm showing the pth of projectile, drw ectors to represent the elocit nd ccelertion of the projectile t n instnt. 2.1 Gien the initil elocit of projectile, clculte the erticl component of elocit t n instnt. 3.1 Using trigonometric clcultions or scle digrm, resole elocit ector into its horizontl nd erticl components. 4.1 Clculte the time of flight of projectile, in cses where the finl height is the sme s the initil height. 5.1 Using the horizontl component of elocit nd the time of flight, clculte the rnge of projectile. 5.2 For projectile lunched from ground height, find, b using smple clcultions or otherwise, the: lunch ngle tht results in the mximum rnge; reltion between the lunch ngles tht result in the sme rnge 6.1 Using the erticl component of the initil elocit nd the ccelertion, clculte the mximum height of projectile. 6.2 Using the time of flight nd the ccelertion, clculte the mximum height of projectile. 7.1 Describe how ir resistnce ffects both the horizontl component nd the erticl component of elocit, nd hence the time of flight nd the rnge. 2 Essentils Workbook Adelide Tuition All rights resered, coping of n pges is strictl prohibited b lw. phsics_prt1.indd 2

2 PHYSICS PHYSICS OF UNIFORM OF PROJECTILE CIRCULAR MOTION CHAPTER The mgnitude of the force of ir resistnce on n Wobject depends on the object s shpe, size, speed, nd surfce texture; nd on the densit of the ir. Appliction: Projectiles in Sport 7.2 Compre qulittiel the force of ir resistnce cting on different objects. 8.1 Describe nd explin the effect of the lunch height of projectile (e.g. shot-put lunched from shoulder height) on the mximum rnge, nd the effect of the lunch ngle for gien height. 8.2 Inestigte the extent to which ir resistnce ffects rious projectiles in sport. Verticl nd Horizontl Components of Velocit Once bod hs been projected into free flight ner the surfce of the Erth, if we neglect the effect of ir resistnce, the onl force cting on the bod is the force of grit (F = mg), cting erticll downwrds. The ccelertion of this projectile is in the sme direction s this force. It is 9-8ms-2 erticll downwrds. Thus, the ccelertion of the projectile is the sme s tht of erticll free-flling object. No ector cn he component perpendiculr to itself. Therefore there is no ccelertion, or component of ccelertion, in the horizontl direction. Thus, no mtter t which ngle the projectile is lunched the horizontl component of its elocit remins constnt. Also the constnt erticl ccelertion, g, is independent of the horizontl speed with which the projectile is lunched. No mtter wht the lunch ngle of the projectile, we cn consider its motion s the combintion of two seprte motions one in the horizontl direction nd one in the erticl direction. Becuse no ector cn he component perpendiculr to itself the horizontl motion nd the erticl motion re completel independent of ech other. Tht is, we cn nlse this two dimensionl motion s the combintion of two seprte independent one dimensionl motions one in the horizontl direction with constnt elocit nd one in the erticl motion with constnt ccelertion = g = 9-8ms-2 erticll downwrds. Thus we cn use ll the tools tht we deeloped lst er in deling with one dimensionl motion with constnt ccelertion, especill Newton s equtions of motion. Use of Multiple Imge Photogrphs We cn use multiple imge photogrphs of projectile s flight to demonstrte tht the horizontl component of elocit is constnt. In n multiple imge photogrph, the time interl between exposures is constnt. We mesure the distnces tht the projectile hs trelled horizontll between successie exposures. If these re the sme then it hs trelled equl distnces in equl time interls nd so its horizontl elocit must be constnt. Fig. 1.1 shows multiple exposure of bsketbll in flight, while Fig. 1.2 is multiple exposure of bll bering projected in the lbortor. Note tht, in both cses, the horizontl distnce between exposures is the sme, indicting tht the horizontl elocit is constnt. Figure 1.2 lso shows bll bering, which is llowed to fll freel t the moment the other bll is projected horizontll. he fct tht the erticl positions of the two blls re the sme shows tht the ccelertion of the projected bll is in the erticl direction nd is the sme s tht of erticll free-flling object. KI 1.3 KI 1.2 KI 1.1 ISO 1.1 Fig. 1.1 Fig. 1.2 Essentils Workbook Adelide Tuition All rights resered, coping of n pges is strictl prohibited b lw. 3 phsics_prt1.indd 3

3 CHAPTER 1 PHYSICS ESSENTIALS STAGE 2 Finding Resultnt Velocit Vectors from their Components ISO 1.2 Gien the horizontl nd erticl components of the elocit of bod, we cn find the ctul elocit of tht bod (both the mgnitude nd direction) b dding the components ectorill. This cn be done either b drwing scle digrm or b sketching the ector ddition tringle nd ppling Pthgors theorem (to find the mgnitude) nd right tringle trigonometr (to find the direction). Drwing the horizontl component ector nd then drwing the erticl component ector with its til on the hed of the horizontl component ector performs the ector ddition. The ector from the til of the horizontl component to the hed of the erticl component represents the resultnt elocit. Fig. 1.3 shows the ector ddition of two elocit components x nd, giing the resultnt elocit. x x Exmple 1 - Finding the elocit ector from its components Find the elocit of bod with horizontl elocit component x = 8ms-1 to the right nd erticl elocit component = 4.6ms-1 downwrd. ISO 1.3 Method 1 Method 2 Scle Digrm Scle: let 1cm represent 2ms-1. x = 8ms-1 4cm nd = 4.6ms-1 2.3cm From the digrm, 4.6cm 9.2ms-1, nd α = 30 = 9 2ms-1 t 30 below the horizontl. Computtion x = = = x = 9 23 tn 4 6 = 8 = = 9.23ms-1 t 29.9 below the horizontl Pth of Projectile ISO 1.4 V The pth of the projectile is prbol. Figure 1.4 shows the pth with the ector representing the elocit of the projectile drwn in t rious instnts in time. Note tht the elocit is t tngent to the prbol t ll times; the horizontl component of the elocit remins constnt throughout the flight the erticl component of the elocit decreses s the projectile rises nd increses s the projectile flls t the top of the motion the erticl component of the elocit is zero. The elocit of the projectile is the horizontl component. Figure 1.5 shows the pth of the projectile with the elocit nd the ccelertion mrked on it t rious instnts in time. Note: tht the ccelertion is constnt nd lws directed erticll downwrd, = g = 9.8ms-2. H V H V H V H H Fig. 1.4 H V V H H V H V Fig Essentils Workbook Adelide Tuition All rights resered, coping of n pges is strictl prohibited b lw. phsics_prt1.indd 4

4 PHYSICS PHYSICS OF UNIFORM OF PROJECTILE CIRCULAR MOTION CHAPTER Determintion of the Verticl Component of Velocit The erticl component of the elocit t n time cn be found b ppling Newton s equtions of motion (for one dimensionl motion) in the erticl direction. Specificll we use the eqution = 0 + t. Find the erticl component of the initil elocit ( 0 or u), nd then ppl this to the erticl motion of the projectile s = u + t, where = 9.8ms-2or 9.8ms-2, depending on which direction we he tken to be positie. Exmple 2 - Finding the erticl component of elocit t n instnt A projectile is lunched with elocit = 48ms-1 t n ngle of 35 boe the horizontl. Find the erticl component of its initil elocit fter 4 seconds. u = sin = u + t = erticl component of elocit = Resolution of Velocit into Components The elocit of the projectile t n point in its flight cn be resoled (i.e. split up) into its horizontl nd erticl components x nd. We need to do this in eer projectile motion clcultion to find the horizontl nd erticl components of the initil elocit. We cn do this using scle digrm. Drw (to scle) ector representing the elocit of the bod. Construct rectngle with this ector s its digonl nd with its sides drwn horizontll nd erticll. The sides of the rectngle represent the horizontl nd erticl components ( x nd ) of the elocit, s shown in Figure 1.6. To find the components computtionll, simple trigonometr gies us x = cosθ nd = sinθ. Exmple 3 - Resoling elocit ector into its components A projectile is lunched with elocit = 48ms-1 t n ngle of 35 boe the horizontl. Find the horizontl nd erticl components ( x nd ) of its initil elocit. Method 1 = 48 sin downwrd Scle Digrm Scle: let 1cm represent 10ms-1. = 48ms-1 4.8cm From the digrm x 3.93cm = 39.3ms cm = 27.5ms-1 = 9 8 (up is positie, down is negtie) q x Fig. 1.6 KI 2.1 ISO 2.1 KI 3.1 ISO 3.1 Method 2 Computtion = cos x = 48 cos 35 = sin = 48 sin x Refer to Phsics Essentils Textbook, Sections 1.1 nd 1.2, for more detiled discussion of horizontl nd erticl elocit components. The fie smple clcultions in Section 1.3 ech demonstrte the resolution of the initil elocit into its horizontl nd erticl components, the clcultion of the ertiwcl component of elocit t some instnt in time, nd the determintion of the elocit from its components. Essentils Workbook Adelide Tuition All rights resered, coping of n pges is strictl prohibited b lw. 5 phsics_prt1.indd 5

5 CHAPTER 1 PHYSICS ESSENTIALS STAGE Time of Flight In situtions where the initil height nd the finl height re the sme, the time of flight cn be found b clculting the time tken for the bod to rech its mximum height nd the doubling it. At the topmost point, the erticl component of elocit is zero. Therefore we cn ppl the eqution = u + t in the erticl direction. Thus u is the erticl component of the initil elocit, = 0, nd = g = 9.8ms-2. Once we he found the time tken to rech the topmost point using this reltion, doubling it gies us the time of flight of this projectile. In generl cses, the time of flight of the projectile cn be found b ppling the eqution s = 0 t + ½t2 in the erticl direction. In this eqution the prmeter s represents the displcement of the bod from its initil position. We need to know the difference in height of the bod between the instnt of lunch nd its finl position s, nd the erticl component of the initil elocit u. We substitute these into the eqution s = u t + ½ t2 nd this ields qudrtic eqution in t which we sole to find the time of flight. Of course, where the initil height nd the finl height re the sme s = 0. ISO 4.1 KI 4.1 Exmple 4 - Finding the time of flight of projectile Find the time of flight of projectile lunched with n initil speed of 48ms-1 t n ngle of 35 boe the horizontl. u = usinθ = 48sin35 = 27.53ms-1, = 9.8ms-2, nd t the topmost point = 0 = u + t 0 = t = 9 8 = 2 81s 9 8t the time of flight is double this i.e. 5.82s Alterntiel the time of flight cn be clculted b relising tht the finl erticl displcement s = 0 s = u t = 27 53t 0 = t( t = 0 or 4.9 t 5 62s 4 9t) 1.5 Mximum Height In ll projectile motion problems, the mximum height boe lunch leel tht the projectile ttins cn be found from the erticl component of the initil elocit nd the ccelertion b performing the following clcultion (in the erticl direction) remember tht t the mximum height the erticl elocit is zero. ISO 4.1 KI 4.1 Thus in Exmple 4 boe the mximum height boe lunch leel cn be clculted s follows: If the time of flight is known, nd if the lunch height is the sme s the finl height, the mximum height cn be clculted b determining the distnce the projectile trels s it flls from the mximum height, using s u t Remember tht t the topmost point the erticl component of elocit is zero (thus u 0 ) nd the time for the projectile to fll is hlf the time of flight. 6 Essentils Workbook Adelide Tuition All rights resered, coping of n pges is strictl prohibited b lw. phsics_prt1.indd 6

6 PHYSICS PHYSICS OF UNIFORM OF PROJECTILE CIRCULAR MOTION CHAPTER Rnge he rnge of projectile cn be determined b multipling the horizontl elocit b the time of flight. The horizontl elocit is constnt. Therefore the horizontl distnce trelled is just elocit times time. Thus, in question (2) (b) of exmple 4 on the preious pge Mximum Rnge nd the Sme Rnge for Different Lunch Angles For projectiles lunched from ground height with gien speed, the mximum rnge results from lunch ngle of 45. Two projectiles lunched from ground leel with the sme speed but with different lunch ngles will he the sme rnge if their lunch ngles re smmetricl, either side of 45, i.e. if the lunch speed is the sme, lunch ngles of (45 α) nd (45 + α) will result in the sme rnge. Alterntiel, rnges will be the sme if the lunch ngles dd up to 90. Both of these sttements cn be shown to be true b smple clcultions, s in the spredsheets in the Phsicl Essentils Textbook, Section 1.4, or proen mthemticll s in the sme section of the Textbook. Refer to Phsics Essentils Textbook, Section 1.4. The fie smple clcultions in this section ech demonstrte the determintion of the elocit of the projectile t n time, the clcultion of time of flight nd the clcultion of rnge for the fie different tpes of projectile motion. 1.6 Effect of Air Resistnce rnge = u x t = ucos t x = u x = ucos = 48cos35ϒ = 39 32ms 1, Rnge = x t = = 257 5m t = 6 55s Air resistnce is force tht retrds the motion of the projectile. The force of ir resistnce lws cts in direction opposite to the direction of motion of the projectile (opposite to the elocit ). The mgnitude of force of ir resistnce depends on the size of the bod, its shpe nd its speed. Figure 1.7 shows the prbolic pth of projectile with the forces of grit Fg nd ir resistnce FAR cting on it on both its upwrd nd downwrd pths. On the upwrd pth ir resistnce hs erticl component F cting downwrd. Thus grit nd ir resistnce both ct together to retrd the erticl motion of the projectile; it comes to erticl hlt more rpidl nd does not rise s fr. On the downwrd pth ir resistnce hs erticl component upwrd, grit nd ir resistnce ct in opposite directions nd so the erticl ccelertion of the prticle downwrd is reduced. Therefore it tkes more time to fll to ground from its highest point. The net effect on time of flight is to reduce it slightl (in the cse of uni-leel projection). Where the bod is projected from some height boe ground leel the net effect of ir resistnce would be to increse the time of flight of the projectile (s it spends more of its time on the downwrd pth where its ccelertion down is reduced b the effect of ir resistnce). The horizontl component of ir resistnce cts opposite to the horizontl component of elocit throughout the motion. Therefore the horizontl component of elocit decreses throughout the motion nd rnge is consequentl reduced. Figure 1.8 shows the flight of projectile, neglecting ir resistnce nd including the effect of ir resistnce. KI 5.1 ISO 5.1 ISO 5.2 KI 7.1 ISO 7.1 F AR F neglecting ir resistnce gf F x F r F AR F F x gf F r including ir resistnce Fig. 1.7 Fig. 1.8 Refer to Phsics Essentils Textbook, Section 1.5 for fuller discussion of ir resistnce nd its effects on the motion trjector of the projectile. Essentils Workbook Adelide Tuition All rights resered, coping of n pges is strictl prohibited b lw. 7 phsics_prt1.indd 7

7 CHAPTER 1 PHYSICS ESSENTIALS STAGE Effect of Air Resistnce ISO 8.1 ISO 7.2 KI 7.2 The mgnitude of the ir resistnce force on n object depends on riet of fctors. The ir resistnce is: directl proportionl to the cross-sectionl re of the bod mesured in plne perpendiculr to its direction of motion;directl proportionl to the squre of the speed of the bod; directl proportionl to the ir densit; depends on the shpe nd the surfce texture of the bod. depends on the shpe nd the surfce texture of the bod. The ir resistnce or erodnmic drg cting on lrge bod moing t high speed through ir cn be gien b R = ½DAρ2, where R is the resistie force, ρ is the densit of ir; A is the cross-sectionl re of the bod mesured in plne perpendiculr to its direction of motion, is the speed of the bod nd D is dimensionless lue (i.e. it hs no units), clled the drg coefficient. The drg coefficient hs lue of bout 0.5 for sphere but cn be s high s 2 for irregulrl shped objects. Note tht ir resistnce increses gretl s the speed of the bod increses, s ir resistnce is directl proportionl to the squre of the speed. Modern crs re designed to he drg coefficients of bout Appliction on Projectiles in Sport For projectile lunched with gien speed nd gien lunch ngle, the greter the lunch height the greter the rnge of the projectile. This cn be seen in Figure 1.9 where three projectiles re lunched with the sme initil conditions but different heights. The greter the lunch height the greter the mximum rnge chieble for gien lunch speed. Howeer s the lunch height increses the lunch ngle necessr to chiee mximum rnge decreses. A lunch ngle of 45 gies the mximum horizontl distnce to point A on the pth, nd so, 45 ields the mximum rnge for uni-leel projection. Howeer s the lunch height increses the projectile spends greter mount of time on its downwrd pth beond point A. Thus, n increse in the mgnitude of the horizontl component of the elocit ields greter rnges, more thn compensting for n decrese in distnce to point A. Thus, s lunch height increses, the lunch ngle for mximum rnge decreses (the decresed ngle ielding greter horizontl component of elocit). A A Fig. 1.9 A Refer to Phsics Essentils Textbook, Section 1A for fuller discussion of ir resistnce nd its effects on the motion trjector of the projectiles in sport. This section lso hs spredsheets with smple clcultions showing the effect of lunch ngle on mximum rnge nd the effect of lunch height on mximum rnge for shot-put. Exmple 5 - The effect of ir resistnce on projectiles in sport A cricket bll is hit from ground leel with speed of 36ms-1 t n ngle of 60 boe the horizontl. It flies distnce of 70.5m. Find the percentge reduction in its theoreticl rnge due to ir resistnce. u x = ucosθ = 36cos60 = 18.0ms-1, u = usinθ = 36sin60 = ms-1, = 9.8ms-2 ISO 8.2 s = u t = t = t( t) t = 0 or 4 9 time of flight = 6.36s theoreticl rnge = x t = s = 114.5m s x 44 0 percentge reduction = = = s x % 8 Essentils Workbook Adelide Tuition All rights resered, coping of n pges is strictl prohibited b lw. phsics_prt1.indd 8

8 PHYSICS PHYSICS OF UNIFORM OF PROJECTILE CIRCULAR MOTION CHAPTER Knowledge nd Skills Checklist Do I know tht the horizontl component of the elocit remins constnt during the flight? Cn I explin wh the horizontl component of the elocit remins constnt during the flight? Do I know tht the ccelertion is erticl, directed downwrd, constnt nd equl to 9-8ms 2? Gien multiple imge photogrph of projectile, cn I deduce tht horizontl elocit is constnt? Gien n pproprite multiple imge photogrph, cn I deduce tht ccelertion is erticl nd the sme s tht of free flling object? Cn I find the horizontl nd erticl components of the initil elocit? Cn I find the erticl component of the elocit of projectile t n instnt? Gien the horizontl nd erticl components of elocit t n instnt, cn I find the mgnitude nd direction of the elocit t tht time? Cn I sketch ectors on the pth of projectile indicting elocit nd ccelertion t n instnt? Cn I clculte the time of flight of projectile if the finl height is the sme s the lunch height? Cn I clculte the rnge of projectile, knowing the time of flight? Do I know wht lunch ngle will ield mximum rnge for projectile lunched from ground leel with gien speed? Gien smple spredsheet cn I recognise from it wht lunch ngle will ield mximum rnge for projectile lunched from ground leel with gien speed? Do I know the reltion between lunch ngles tht will result in the sme rnge for projectiles lunched from ground leel with gien speed? Gien smple spredsheet, cn I recognise from it the reltion between lunch ngles tht will result in the sme rnge for projectiles lunched from ground leel with gien speed? Do I know wht ir resistnce is nd the direction in which it cts? Do I know, nd cn I explin, the effect tht ir resistnce hs on the erticl component of the elocit of projectile? Do I know, nd cn I explin, the effect tht ir resistnce hs on the horizontl component of the elocit of projectile? Do I know, nd cn I explin, the effect tht ir resistnce hs on the time of flight of projectile? Do I know, nd cn I explin, the effect tht ir resistnce hs on the rnge of projectile? Cn I sketch digrms showing the trjectories of projectile neglecting ir resistnce nd with ir resistnce tken into ccount? Gien n pproprite spredsheet, cn I deduce the effect of lunch height on rnge, for projectile lunched with gien speed? Do I know the effect of the lunch height on the mximum rnge of projectile? Gien n pproprite spredsheet, cn I deduce tht the lunch ngle necessr to ield mximum rnge decreses s lunch height increses for projectile lunched with gien speed? Cn I explin wh the lunch ngle necessr to ield mximum rnge decreses s lunch height increses for projectile lunched with gien speed? Gien n experimentl lue for rnge, cn I describe the extent to which ir resistnce ffects rious projectiles in sport? Further Questions: Refer to Essentils Reision Guide. Contins extensie supplementr topic questions, the lst 4 ers exms with full solutions nd suggestions. For more informtion isit: Essentils Workbook Adelide Tuition All rights resered, coping of n pges is strictl prohibited b lw. 9 phsics_prt1.indd 9

9 CHAPTER 1 PHYSICS ESSENTIALS STAGE Exercises NOTE: tht the ccelertion is constnt downwrds, becuse the grittionl force on the bll is constnt downwrds 1 A bll is thrown horizontll from cliff with speed of 10ms-1, s shown in the digrm t right. Neglecting the effect of ir resistnce nd tking grittionl ccelertion to be g = + 9-8ms-2, sketch grphs (on the xes below) to show () the horizontl speed x of the bll ersus time, for the durtion of its flight; (b) the erticl elocit of the bll ersus time, for the durtion of its flight. 1 10ms x t t Air resistnce pplies force in the opposite direction to the bll's elocit. Thus, both the erticl nd horizontl components re ffected (c) On the sme xes, sketch grphs to show the horizontl speed nd the erticl elocit ersus time if ir resistnce hs significnt effect on the flight of the bll. Lbel ech grph clerl to distinguish it from the preious grph. 2 On ech of the two projectile trjectories depicted below, drw ectors to show the directions nd reltie mgnitudes of the elocit nd the ccelertion of the projectile t ech of the points A, B & C. B A B C A C NOTE: tht the elocit of the projectiles constntl chnges downwrds, becuse the force of grit on the bll is constntl downwrds. 3 A tennis pler hits bll horizontll t 35ms-1 when it is 1-6m boe the ground. () Clculte the time of flight of the bll. See Newton's second lw in Chpter 4 (b) If the bll is hit 11-0m from the net determine, b clcultion, whether the bll will cler the net which is 0-9m high. 10 Essentils Workbook Adelide Tuition All rights resered, coping of n pges is strictl prohibited b lw. phsics_prt1.indd 10

10 PHYSICS OF PROJECTILE MOTION CHAPTER 1 4 The multiple imge photogrph on the right shows the motion of two blls A nd B tht re relesed t the sme time from the point O. Bll A flls freel while bll B is projected horizontll. () Using mesurements from the digrm, explin how it shows tht the horizontl elocit of B remins constnt. (b) Explin how we cn use the photogrph to deduce tht the elocit of bll A increses during its fll. (c) Explin wh bll B hs no ccelertion in the horizontl direction. (d) Bll A is flling freel nd hs erticl ccelertion g = 9.8ms-2. Using the photogrph determine the erticl ccelertion of bll B. Explin how ou got our nswer from the photo. (e) Deduce which bll will hit the ground with the greter speed. Essentils Workbook Adelide Tuition All rights resered, coping of n pges is strictl prohibited b lw. 11 phsics_prt1.indd 11

11 CHAPTER 1 PHYSICS ESSENTIALS STAGE 2 5 A prcel is to be dropped from n eroplne to bot t se. The eroplne is fling with speed of 100ms-1 t fixed ltitude of 120m boe se leel. () Clculte the erticl distnce tht the prcel flls in the first two seconds. (b) (i) Clculte the erticl elocit of the prcel fter two seconds (ii) the elocit of the prcel fter two seconds The constnt erticl ccelertion is independent of the horizontl speed. (c) Explin wht hppens to the two components of the elocit, the horizontl nd the erticl, of the prcel s it flls to the wter. (d) Clculte the time, from the moment tht it is relesed, for the prcel to hit the wter. (e) in Clculte the distnce, from the bot, t which the prcel must be relesed so tht it lnds the wter ner the bot. 12 Essentils Workbook Adelide Tuition All rights resered, coping of n pges is strictl prohibited b lw. phsics_prt1.indd 12

12 PHYSICS OF PROJECTILE MOTION CHAPTER 1 6 At point on the upwrd pth of projectile the elocit of the projectile is 18ms-1 t 40 boe the horizontl, s shown in the digrm. () Find the horizontl nd erticl components of the elocit t this point. (b) Describe how (nd explin wh) these components of elocit will chnge oer the rest of the flight. (c) Stte the elocit of the projectile t point X. 7 A gun, imed horizontll, fires bullet with speed of 900ms-1. The gun is 2m boe ground leel. The time of flight of the bullet is 0.64s. () Find the rnge of the bullet. (b) Find the elocit with which the bullet hits the ground. Velocit is ector quntit, it requires both mgnitude nd direction Essentils Workbook Adelide Tuition All rights resered, coping of n pges is strictl prohibited b lw. 13 phsics_prt1.indd 13

13 CHAPTER 1 PHYSICS ESSENTIALS STAGE 2 8 A mortr shell is fired from ground leel (t point A on the digrm) with elocit 0 = 100ms-1 t n ngle of 80 boe the horizontl. () Clculte the horizontl nd erticl components of the elocit of the shell t the instnt it is fired. B 0 A 80 (b) Clculte the erticl component of the elocit (i) one second nd (ii) thirteen seconds fter firing. (i) (ii) (c) Clculte the resultnt elocit of the shell fter 13 seconds. (d) Stte the elocit of the shell t point B. (e) Stte the ccelertion of the shell t point B. (f) Determine the mximum height chieed b the shell. 14 Essentils Workbook Adelide Tuition All rights resered, coping of n pges is strictl prohibited b lw. phsics_prt1.indd 14