Answers to Chapter 1 & 2

P1.41 EMBED Equation.DSMT4 We observe that EMBED Equation.DSMT4 .EMBED Word.Document.8 s mergeformat FIG. P3.19 So EMBED Equation.DSMT4 . The diagram shows that the angle from the x axis can be found by subtracting from 180 EMBED Equation.DSMT4 . P1.45 (a) EMBED Equation.DSMT4 (b) EMBED Equation.DSMT4 (c) EMBED Equation.DSMT4 (d) EMBED Equation.DSMT4 (e) EMBED Equation.DSMT4 EMBED Equation.DSMT4 P1.47 EMBED Equation.DSMT4 FIG. P3.59 P2.3 (a) EMBED Equation.DSMT4 (b) EMBED Equation.DSMT4 (c) EMBED Equation.DSMT4 (d) EMBED Equation.DSMT4 (e) EMBED Equation.DSMT4 P2.5 (a) at EMBED Equation.DSMT4 , EMBED Equation.DSMT4 (Point A) at EMBED Equation.DSMT4 , EMBED Equation.DSMT4 (Point B) EMBED Equation.DSMT4 (b) The slope of the tangent line is found from points C and D. EMBED Equation.DSMT4 and EMBED Equation.DSMT4 , EMBED Equation.DSMT4 .EMBED MSDraw mergeformat FIG. P2.7 (c) The velocity is zero when x is a minimum. This is at EMBED Equation.DSMT4 . P2.11 (a) Acceleration is constant over the first ten seconds, so at the end, EMBED Equation.DSMT4 . Then EMBED Equation.DSMT4 so v is constant from EMBED Equation.DSMT4 to EMBED Equation.DSMT4 . And over the last five seconds the velocity changes to EMBED Equation.DSMT4 . (b) In the first ten seconds, EMBED Equation.DSMT4 . Over the next five seconds the position changes to EMBED Equation.DSMT4 . And at EMBED Equation.DSMT4 , EMBED Equation.DSMT4 . P2.17 (a) EMBED Equation.DSMT4 becomes EMBED Equation.DSMT4 which yields EMBED Equation.DSMT4 . (b) EMBED Equation.DSMT4 P2.21 (a) EMBED Equation.DSMT4 , EMBED Equation.DSMT4 , EMBED Equation.DSMT4 so EMBED Equation.DSMT4 , EMBED Equation.DSMT4 so EMBED Equation.DSMT4 . Thus EMBED Equation.DSMT4 and EMBED Equation.DSMT4 . (b) At this acceleration the plane would overshoot the runway EMBED Equation.DSMT4 . P2.23 In the simultaneous equations EMBED Equation.DSMT4 we have EMBED Equation.DSMT4 . So substituting for EMBED Equation.DSMT4 gives EMBED Equation.DSMT4 EMBED Equation.DSMT4 . Thus EMBED Equation.DSMT4 . P2.27 Take the original point to be when Sue notices the van. Choose the origin of the x-axis at Sues car. For her we have EMBED Equation.DSMT4 , EMBED Equation.DSMT4 , EMBED Equation.DSMT4 so her position is given by EMBED Equation.DSMT4 . For the van, EMBED Equation.DSMT4 , EMBED Equation.DSMT4 , EMBED Equation.DSMT4 and EMBED Equation.DSMT4 . To test for a collision, we look for an instant EMBED Equation.DSMT4 when both are at the same place EMBED Equation.DSMT4 From the quadratic formula EMBED Equation.DSMT4 or EMBED Equation.DSMT4 . The smaller value is the collision time. (The larger value tells when the van would pull ahead again if the vehicles could move through each other). The wreck happens at position EMBED Equation.DSMT4 . P2.29 (a) EMBED Equation.DSMT4 EMBED Equation.DSMT4 when EMBED Equation.DSMT4 , EMBED Equation.DSMT4 . Therefore, EMBED Equation.DSMT4 . (b) EMBED Equation.DSMT4 EMBED Equation.DSMT4 P2.31 (a) EMBED Equation.DSMT4 EMBED Equation.DSMT4 and EMBED Equation.DSMT4 . (b) EMBED Equation.DSMT4 EMBED Equation.DSMT4 uvUlbd,M15m,Ma_qar Xz@_io2nTnVwVs0pYqmAeg.pCA_2wSGvYSUeaWN(UeQQzudJOx HIr,1rwvU 2HlBi7HsBH3swYbE4tI5zIco xa/J(ETDL4d/o7o. GfbnNl( HWnQ39FxHDzTQ)CtOi2vR h4Q.t.bOyA06-zByYowKnW60VZLD5wZJjAPZcT2U0P7H4orA,YDx8hvqz8WqAU SSEeZzr,UdLwl)wjHQ(kO1sYCuvI yjOr23IMEFJ/UmVdd7jl 00aC0aC0aC0aC0a(toJ)m_BlGvCqw4CdpoY)Cc(,89CEsbdr(L9)oBcLp/)(DSgpLe0R/36u1YTn87s ZivqG9DBv8 E/vnd.Yf2MCa-nLCCYZAv,C/) zaO(4t2Il8scamj0 2LE,yAdks /8o)C6089h/ cO waC 1Ui-.26 rC Fm D0r2d(gPXs3ySy3F959ao0i78s- OYz7dPjEY7cVu7VWoa((PEaaOj 0NI1gYjQf 52- Q.2gS0A3,e(bE(/Xukj3f3QoX CsNI(h)@(6 afhF (ak0f13ngZ3fderlJW-r)2YN/m2bJb-Nj 3C6u@IBe4zfY3aBSU1UaixjY7uX5.J1af5_UJw uQqY5te.5xN5qMp7mMrEa4@a7ZEfCi3TPd(lo2MD0eQP224g ,DCe1C932B3T2k1 Eoo31WfCDC0dKg(DCof0fCof0fmf0f_3R5ppJ03.nr3p7DD(Q00JPff0(KD0CCJT4y3Yf.aWbJUJbaKf) oaBXfKGeHODM7K C(k7@NZLCdWbRQUfhHe_q6h43aTD2TSQmfL CRRO3obT16Dx0pYn/MXuxaW10kbgYS0eDtoaODkX-7-0 q vMlX2CnT17fg WfiSJm1MOo-lg 3yk7dDlwMqW3_hT(18z_jbuVFl78/FhK-D2sevkmpXpkDPzEjzgD0Ln.@vHDubORTV0-S2Fac3cZ c_VJbGg_I3CDa)T(7sq(H2fC 2UmUDCfCPgeUEeF.O5)33CXYC,jsOB9c(dZBsTDePD2P l,nCaXHAC0,E,w ZmiW0c3NfV 3/Kc(0dUkpafqJQ 97 /CF9oGC7W0fxhos2dTJ bRw_ac0/kfSaJ-37i/CVP_oR )0,ZYuYF/@Cm5cUa2pmtfWf8( EC 4phxaWh4Ys8tDH8l8yOcdJxNP r4,s2m)_/fj O3duJx4aa853w hc a,coozfyZRzKLK e/-yyUxcGRpWj0GyBq 4sLhY7t0goJaJparM6UCq Oc5o/I_KC C_ aeOp90xml9bFOZPOkTl2 kJboCya(2eCZ2eDp(PeCya(2Q)p2E0BC(PeCya(/CBa(/Cv E(PeCya(2JhCa(P0(Py0(P0(P)0x 6nC2-DyJeCZ 02tPWkX0(PaCQjNC2XWiUEyQhH4T45VgecOOc(WHCj24cxugxlp7rFXp@c-Ew85Vya0rC4F3C4 vg56HW6 Fwhfaj00RcG1PnHEO5BB4ns_Z3C_Z0z3w3LwhpCbtnaHcx6a3A icRcynqiCsCJKoG6dAju46F_FvGBzkE. Qnp2-DUQC(7jhi0t6 - eea(7la  RCF RCQmh00,6d DaaPlhn bCCeR70,7J RaVaaPjh,  RCkQhhaJCsQvhhaFCQghaBCQvghF2dpufpm6hpeFjpVl240(10(140(1NjP0v040l(7e(2lpWl0yCbQohm0aS9uxxb0ppcehL9-iCe0p8B5 /xrCHIujxm, 8MrhMVbwQ(z- -Q0C b@k.aF9CpCa9Pj bCo40a(6C nDT,mJr4cRBYd0Jg.3S0ChtWQ dhJOStz4d70o0cS.b 9ts6ovDWZD9F,Ndo .JPj_CHER(Nw,fJuX78ScCIYMrDqWAerq6nKsI,OP4o.3.FlcyvtVURl,zR.,WxImY)Inaxc2QKCiENDfEwSV1Bajb2/ZG(/igR7vW _3yklY2f2RWZmdB6jM2hVjCMbH5zVz-eK)ub,i-B DPz6KkMBoipRvmFCzAi W2eBj7wvn.,pOv,dySZ,rlky Wwn9 c8484(gzsiabmmooiL.4HFb8jw(3v4UF79 f9f_g,-DwK(Eyk0f. a2b4J_/G-ip2 tt/7hEZUc0Zi_666qFCXcaenta7Xgf8)Iv61(cQTQ-965vXvFh wX5yNGnLah/aa3I2FYu2 qg_WOX8 bRjt7wwjSR 6sJtA.Ti.L5h iJ7oY3-M178ELd72FwFZr1nCxUQWRjqKZXxie9docPSCF.k6@6gCt4(4sYSu6tAZ2Ois8LaYNEAv/w Ya kd R2KoS5jUCw_S5ta_5)p3KWsVaZWIGYa990Ceqp8rcKd 6qCvv8hyNGZJrt,6@bPbLXIZ.Eo@K_YhR LBQLy dGJyhTr3ab lW icZi21zuF7XDc1,g8BtFXI4xWoTRWZ4QFX.RT aUUK_I NYE8 VJN(nc 11fCiHANx TJZUF AH(r.)bxChkWQv OcOmDldI , 6NqK YkA/7xS@akMl5mx 1pmbVMXWHH8NjiqkrZfwqUkV-7c/7c xRbKVWqZE8Zpq-V20F, PXyf-43wN c2Fin 6bcH,z35 ,DXQbFu(Di5MoO k735,c jycA1Cy)t/dQacMEdzef4 cnyq7R4Kvgg_V7OIC3cb2nK4Y7l- )xpK)z2l)Mku9dRWl/rg.wWjs cVGet,5yod Nez56jPPeoWi54dx02uxhr Sr F(s (s)8o-ORXBQP2DSF_hj,l_HwgTwLq@uzEgtWqdnO0ggtTUvGGUpa0SRzZSRd0d7kCOk xxxx(pxIAp/G6G xOdTVx8xcHHA I1YlW H65n/)jo 0hQUOAtxpQASBxQQFBax-2 P0FG(xV- P@Pax z) Qa0BFGCGxh_cv@yx-6Qa0fFGW cVa cTatzL/NApWya0jFG9(TRcza4L)L Q105y/rGUcl@QF c Fc1GV4KDbD8nFLAypWF0ZnzWi/_@4-/bWayp_ z89wQx1QkYux_wxDh,F p@yxVnf R0@,aU0j_X/xcxfT.k)axFm_Qcn GvQn_mo1K )_1 Dl6_,Zdr6wgigVdXYXGuuGVH6 0l0fy1 0R(/kKAA@V X3@CdTl HcU4OWKgvjnW4mGtPlT,fC-PpvfgA0hIN-.g0g2zX7c9eE7Vqk_Acd0jw/KSYJxD nZj 3h 0 nPDfZLCej N.x1Y(LJWoj9MsJoXJ ,Gg/XkVn ,W ,7r0/XtVi9ies9lvY1PaOayGOga/vsZoYivZef (g1znaW1@4R-rDggk N/tTasgKixC4CfGOjq-4Y9hwG9ZP(1NGx.-3Iya sPsuKc,E.Wo-jE3WXDvvlu5zuR8ohalraY8YqDIC66fuR_XfO ePMd,Ydc jy4WQPMfTVU4o_hkCmdDT/6 xXikuTCVpXMCE D5RpcY3 O@7wec5wgDECC( CZkoCMmEm Vc E0(GhA2taH sEm1VL@)z OF fIyhQakt@BQ7f 00aCC -w,m3MopVjHk6aVFS_9xYnOJ3429CnprD z Oh6bh9C2F24Cyz-anf8MJ55apbje8WCmhht0chRycBpA 44J8t5rlu6WryMsYd6jgQ1imHC1q Cpu6PfGihfghb84Cu_g2LgHPrhGwlNYm-exU,Lv_@90)i eW CT,T.C0rkn r-PCaapmrCpa-XKZVb fjHTQUr00VaprXrXrXjhe0lZoI95b7khCS5J0 NY)WyPCr6C/m941 zI AkHgHyScY09KYKbKDC84HiK4R3kv(LJy6m 7lX0nY6Wo(0CCvm.LPwpkE_wlV.md@,pwy)B p9fZ62u6dm2x b)Bip@,STmRbeQ8dIxIIY2mJc66Mzs kBi0V9JjxxiI6Ry SKL0 4JQ5YRChU357 HSf uKhfy sadvfrs_@k Y(ofg74B2YgP I @Nm8M0r06snCYhv0J3g9 aTY Fh0P csa9 bCS98a KI dm0TMfbR9aQTAaxG0(sPx0TH@cH ZaCc Lfehq 8e8ofHe DI(6Iq5nColXj9yHP 7 M)CiXp9Yb KNulc44)61,cJq0pCg50,pE2uAF SyE2nfHH@8qs1K-C6t pTHQj047W9QWp 5.M5o(.K 0 )79 i,KgXS/ C)P E1WehJ4( bCTE1K9amHdNdX9,r WnRVWs bHRDRd(5R4c9TuNC)Ma15aaT. / vmnUzCCKu9zuHU/Fwpa Yp6P77lnoxpkm3njra8EKLMMCglg(a0hny U0)BIQS vL.z2407w3.VaWD-m j8js(m),WGpW/ru71KI3Zrxid3rhn.1a1dAC pNm -q2PcvCaj oFvoCbu4C ,YZ yaw 1np/oX0WUEbk0UQ9RfWD-- 5I5 SNMmSapPCaa00ThH0tjv2r00ZScCYen.WRcRxjzyys9Yh..ZmG0,H-  ut93 .1rCaaa00r0PJCXcxpa08oEo64C Ca0fPCFpl52HCrCF0Dmc8FCCTFir8c( grs3f5H9Ck C (2DYd(yP5 PaxW9 QuscUkKr4CipmPHCl68l6p4NcCGqG/5ml1DNG3NCzdlb ,dhaxpmpHCalaw4d16muyNCR)0760D NFLJbmDr5JuGX.jnzk71F.KdJkp4pngtr VjQd6 QbnJf)JAqXTTV-W))VK-F HZaLFdHGr7Op@Pib,y,InDLdPDmmi06 v9B905r_O5Chb Ryx( ZkVB42T)BuR SeS @7WmaFZXFpJ/6 TpWSBItoUBUHO4TzeRJ7sbN)P6_6P_0zO)OmsVheEwGlsSQlmwzH6qkL12_@0oVPQoF2Sg4E0ghEc8 aLTATFwR,an50wIVhKz,xnY L m 40rCLx Hxf8hFbdMLyDX4z/h6ClUPHdWWpRtzM.6Y8T.ZMtnIvLrNN xsgPScq(UCkzazGktvO.ZfHkh9kF0-8 _TF8hz@bmb4Y ) kg E@VOn27_2dJ19F0BcqaXDOG1 cX149AEYjorV@1jAC)PBIVxsP 6nz2SwNarbfM.x_y C4QWJI-EuCqO,up 8a2uF0CCBZl6_QX cFz14BdZ4 5 O4lEfLRWQ-9w-FKI 2inNkq5Z669HDo1vKYd775J S2JGVQh,JJm)YTUlZWlllQTqLf6GW2bmSlWTvyc ,86pfxQ33jxo v 40U9xpHeAM AZDhDy_uMx9w3sf98YLJqJyJvQY1(2gOVo3,9Z Ix c_X-r_z loAwWBR9NS/vWWL_4QTL76C2iSbfJz_XnOyjYykFtUjZcUZgUI lqDaTPIjbji 0DxZ igfXjpThvym bOeAwEpT7WSWW5O@nfkkMZy9fj2e2KddnW04R1x z5dIYP3qEeZE6mk uGTavPcu 8ZhC mdo/OAW ffD1EFt.aJHqcty2-/7gP7T 6kcc1-116C jejHjjxIh9bHKi, f3keY2SREDo3FO9@/LvEZwTI.vHYj7Q3 xhA/Y9f n@4IClILQHHbtHzHi8I ur c.zY7rgma F/ ltx6GJ96jxM4)aizTmmSJOYfY5 T.l/EIJhsB/8NIsqiGox qs0sWYIpcD ri- UkAKraHsn )3FZ D)8VNvDQFd62RNM4YS4MEF,2-og/tJZxR_sDuNQ_HjWakZb,)EyZm65YFP K 4vQF9JViZzSZPnvj6_SGJywh..ir/Q@8IMwy6sMVVG5aY6NkWJDerrot1XFSwNwV,/-,Ps.5 6bGG_o s((Es, A@77o0 pl B/ 7ya, 7NOoWG yV uuuUCyNm_xVi 7,o13,rPCo0M1C95clcws90lZ 0nxOn-6-1K-rpN-gklb86XD 1yTJRN7 wH xCovdb HJLuVwF8d2 PCBV03Tg1.8 ,Y 7U(gpm Oqh3vz- xeq35gF74 0 vB6X KUG81vs,S9 qp zB@ HOm7i5jiU8xkL2L.WMleFJ32IM. EKHl5fNxHVEKy9Jdnm 1ktn-iI aOtHAbtZVPdGdz-JlL5Kc9HbQsn1T(dRX/ 5xLbR Y@h0-3D(GHB(DPntBEpRexJA6 /7H4 i8uG02)Sc5 ig7 /xrBGB1oyttke3 w7LupKUwFmfAevMsDUvRDHURGb6IN2o-/GQ2M37K5z0rjrgi929_7 8sZws I_8IX)Q0U M i9iE)EO xJ(4Poy3yQ@M_DQF_)NEG3mo@W8flBgsKhX90wPHrf)ZF3y