Qhov nrug, feem ntau muab qhov sib txawv "s", yog ntsuas qhov chaw uas yog kab ncaj nruab nrab ntawm ob lub ntsiab lus. Qhov nrug tuaj yeem hais txog qhov chaw nruab nrab ntawm ob lub ntsiab lus tsis hloov pauv (piv txwv li, ib tus neeg qhov siab yog qhov deb ntawm hauv qab ntawm ko taw mus rau saum taub hau) lossis nws tuaj yeem hais txog qhov chaw nruab nrab ntawm txoj haujlwm tam sim no ntawm cov khoom txav thiab thawj qhov chaw uas lub hom phiaj pib txav mus. Feem ntau cov teeb meem nyob deb tuaj yeem daws tau los ntawm qhov sib npaug s = v × t, qhov twg yog qhov nrug, v yog qhov nruab nrab nrawm, thiab t yog lub sijhawm, lossis siv s = ((x2 -x ib1)2 + (yov2 -ib y1)2), qhov twg (x1, y ua1) thiab (x2, y ua2) yog x thiab y tswj hwm ntawm ob lub ntsiab lus.
Kauj ruam
Txoj Kev 1 ntawm 2: Xam Qhov nrug Nrog Qhov Nruab Nrab Ceev thiab Sijhawm
Kauj Ruam 1. Nrhiav qhov nruab nrab nrawm thiab sijhawm
Thaum sim suav qhov deb uas cov khoom txav tau mus, muaj ob daim ntaub ntawv uas tseem ceeb rau qhov kev suav no: ceev (lossis tshaj tawm) thiab sij hawm tias qhov khoom txav mus los. Nrog rau cov ntaub ntawv no, nws tuaj yeem suav qhov kev nrug deb ntawm cov khoom siv cov mis s = v × t.
Txhawm rau nkag siab cov txheej txheem ntawm kev siv cov lej sib nrug, cia peb daws qhov piv txwv teeb meem hauv ntu no. Cia peb hais tias peb tab tom taug txoj kev ntawm 120 mais ib teev (kwv yees li 193 km ib teev) thiab peb xav paub tias peb yuav nyob deb npaum li cas ib nrab teev. Siv 120 mais ib teev raws li tus nqi ntawm qhov nruab nrab nrawm thiab 0.5 teev raws li tus nqi ntawm lub sijhawm, peb yuav daws qhov teeb meem no hauv cov kauj ruam tom ntej.
Kauj Ruam 2. Muab qhov nruab nrab nrawm nruab nrab ntawm lub sijhawm
Tom qab paub qhov nrawm nruab nrab ntawm cov khoom txav mus los thiab lub sijhawm nws tau mus ncig, suav qhov kev mus kev deb yog qhov yooj yim. Tsuas yog muab ob qhov txiaj ntsig los nrhiav cov lus teb.
- Txawm li cas los xij, nco ntsoov tias yog chav tsev ntawm lub sijhawm siv hauv tus nqi nruab nrab nrawm txawv ntawm qhov siv hauv lub sijhawm, koj yuav tsum hloov pauv ib qho kom phim. Piv txwv li, yog tias peb muaj tus nqi ntsuas nruab nrab ntsuas hauv km ib teev thiab lub sijhawm ntsuas hauv feeb, koj yuav tsum faib tus nqi lub sijhawm los ntawm 60 kom hloov nws mus rau teev.
- Cia peb ua tiav peb qhov teeb meem piv txwv. 120 mais/teev × 0.5 teev = 60 miv. Nco tseg tias cov koog nyob hauv lub sijhawm tus nqi (teev) tsis suav tus lej ntawm qhov nruab nrab nrawm (teev) tawm hauv tsuas yog cov chav nyob nrug deb (mais).
Kauj Ruam 3. Hloov cov kab zauv los xam lwm qhov sib txawv
Qhov yooj yim ntawm qhov yooj yim nrug qhov sib npaug (s = v × t) ua rau nws yooj yim siv qhov sib npaug los nrhiav tus nqi ntawm qhov sib txawv uas tsis yog nrug. Tsuas yog cais qhov sib txawv uas koj xav pom raws li txoj cai yooj yim ntawm algebra, tom qab ntawd nkag mus rau qhov tseem ceeb ntawm ob qhov kev hloov pauv kom pom tus nqi ntawm qhov sib txawv thib peb. Hauv lwm lo lus, txhawm rau laij cov khoom qhov nruab nrab nrawm, siv cov zauv v = s/t thiab txhawm rau suav lub sijhawm dhau los ntawm qhov khoom, siv qhov kev ua zauv t = s/v.
- Piv txwv, cia peb hais tias peb paub tias lub tsheb tau npog 60 mais hauv 50 feeb, tab sis peb tsis muaj tus nqi rau qhov nrawm nrawm li qhov khoom txav mus. Hauv qhov no, peb tuaj yeem cais qhov sib txawv v hauv qhov yooj yim sib nrug deb kom tau v = d/t, tom qab ntawd tsuas faib 60 mais/50 feeb kom tau txais cov lus teb 1.2 mais/feeb.
- Nco ntsoov tias hauv qhov piv txwv, cov lus teb rau kev nrawm muaj qhov txawv txav (mais/feeb). Txhawm rau kom tau txais cov lus teb hauv ntau mais/teev, sib npaug los ntawm 60 feeb/teev kom tau txais txiaj ntsig 72 mais/teev.
Kauj Ruam 4. Nco tseg tias qhov hloov pauv "v" hauv cov qauv ntsuas nrug yog hais txog qhov nrawm nruab nrab
Nws yog ib qho tseem ceeb kom nkag siab tias cov lej yooj yim nyob deb muab cov lus pom yooj yim ntawm cov lus tsa suab ntawm ib yam khoom. Cov qauv nyob deb xav tias ib yam khoom hauv kev txav chaw muaj qhov nrawm nrawm - hauv lwm lo lus, nws xav tias cov khoom hauv kev txav muaj ib leeg, tsis hloov pauv. Txog teeb meem lej lej, xws li cov uas koj tuaj yeem ntsib hauv kev teeb tsa kev kawm, nws qee zaum tseem tuaj yeem ua qauv kev txav ntawm cov khoom siv qhov kev xav no. Txawm li cas los xij, hauv lub neej tiag tiag, cov piv txwv no feem ntau tsis cuam tshuam qhov txav ntawm cov khoom txav mus, uas qhov tseeb tuaj yeem nrawm dua, qeeb, nres, thiab thim rov qab rau lub sijhawm.
- Piv txwv li, hauv qhov piv txwv teeb meem saum toj no, peb xaus lus tias kom npog 60 mais hauv 50 feeb, peb yuav tsum taug kev ntawm 72 mais ib teev. Txawm li cas los xij, qhov no muaj tseeb tsuas yog taug kev ntawm ib qhov nrawm thoob plaws tag nrho cov lus. Piv txwv li, los ntawm kev ncig 80 mais/teev rau ib nrab ntawm txoj kev taug thiab 64 mais/teev rau ib nrab ntxiv, peb tseem yuav npog 60 mais hauv 50 feeb - 72 mais/teev = 60 mais/50 feeb = ?????
- Kev suav daws raws cov kev daws teeb meem uas siv cov khoom sib txuas feem ntau yog qhov kev xaiv zoo dua li cov qauv nyob deb rau kev txheeb xyuas qhov khoom qhov nrawm hauv qhov xwm txheej tiag tiag vim tias muaj kev hloov pauv nrawm.
Txoj Kev 2 ntawm 2: Xam Qhov Nruab Nrab Ntawm Ob Lub Ntsiab Lus
Kauj Ruam 1. Nrhiav ob qhov chaw ua haujlwm ntawm ob lub ntsiab lus
Yuav ua li cas yog tias, es tsis txhob suav qhov deb uas cov khoom txav tau mus, koj yuav tsum suav qhov deb ntawm ob yam khoom tsis hloov pauv? Hauv qhov xwm txheej zoo li no, tus lej raws qhov nrawm uas tau piav qhia saum toj no yuav tsis ua haujlwm. Hmoov zoo, cov qauv sib txawv tuaj yeem siv los xam cov kab ncaj ncaj nrug ntawm ob lub ntsiab lus. Txawm li cas los xij, txhawm rau siv cov qauv no, koj yuav tsum paub txog kev ua haujlwm ntawm ob lub ntsiab lus. Yog hais tias tuav ib txoj kab nrug deb (raws li ntawm tus lej kab), kev tswj hwm yuav suav nrog ob tus lej, x1 thiab x2. Yog tias koj tab tom tuav qhov nrug ntawm ob qhov ntev, koj yuav xav tau ob qhov tseem ceeb (x, y), (x1, y ua1) thiab (x2, y ua2). Thaum kawg, rau peb qhov ntev, koj yuav xav tau tus nqi (x1, y ua1z, xav1) thiab (x2, y ua2z, xav2).
Kauj Ruam 2. Xam qhov nrug ib leeg los ntawm kev rho tawm qhov ua haujlwm sib npaug ntawm ob lub ntsiab lus
Xam qhov deb ib seem ntawm ob lub ntsiab lus thaum koj twb paub tus nqi ntawm txhua lub ntsiab lus yog ib qho yooj yim. Tsuas yog siv cov mis s = | xwm2 -x ib1|. Hauv cov mis no, koj rho x1 od ua x2, tom qab ntawd coj tus nqi tseeb ntawm koj cov lus teb kom pom qhov deb ntawm x1 thiab x2. Feem ntau, koj yuav xav siv tus lej ib qhov deb nyob deb thaum ob lub ntsiab lus nyob ntawm kab lossis tus lej.
- Nco ntsoov tias cov mis no siv qhov tseem ceeb (cim " | |"). Tus nqi tsis muaj txiaj ntsig tsuas yog txhais tau tias tus nqi sab hauv lub cim ua qhov zoo yog tias nws tsis zoo.
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Piv txwv li, cia peb hais tias peb nres ntawm ib sab ntawm txoj kev ntawm txoj kev ncaj nraim. Yog tias muaj lub nroog 5 mais pem hauv ntej ntawm peb thiab lwm lub nroog 1 mais qab peb, ob lub nroog nyob deb npaum li cas? Yog tias peb teev lub nroog 1 ua x1 = 5 thiab nroog 2 li x1 = -1, peb tuaj yeem suav s, qhov nruab nrab ntawm ob lub nroog, raws li hauv qab no:
- s = | xwm2 -x ib1|
- = |-1 - 5|
- = |-6| = 6 miv.
Kauj Ruam 3. Xam qhov nrug ob sab siv Pythagorean theorem
Xam qhov kev ncua deb ntawm ob lub ntsiab lus hauv qhov chaw ob seem yog qhov nyuaj dua li hauv ib seem, tab sis tsis nyuaj. Tsuas yog siv cov mis s = ((x2 -x ib1)2 + (yov2 -ib y1)2). Hauv cov qauv no, rho tawm ob x-kev sib koom tes, xam cov hauv paus square, rho tawm ob y-coordinates, xam cov hauv paus square, tom qab ntawd ntxiv ob qhov txiaj ntsig ua ke thiab xam cov hauv paus cag kom pom qhov deb ntawm ob lub ntsiab lus. Cov mis no siv rau ob lub dav hlau dav dav - piv txwv li, ntawm daim duab x/y tsis tu ncua.
- Cov txheej txheem nyob deb ntawm ob sab ua rau siv Pythagorean theorem, uas hais tias qhov ntev ntawm hypotenuse ntawm daim duab peb sab ntawm sab xis yog sib npaug rau cov hauv paus hauv paus ntawm lub xwmfab ntawm ob sab.
- Piv txwv li, peb hais tias peb muaj ob lub ntsiab lus hauv x -y dav hlau: (3, -10) thiab (11, 7), uas sawv cev rau nruab nrab ntawm lub voj voog thiab taw tes rau ntawm lub voj voos, feem. Txhawm rau nrhiav txoj kab ncaj nruab nrab ntawm ob lub ntsiab lus, peb tuaj yeem suav nws raws li hauv qab no:
- s = ((x2 -x ib1)2 + (yov2 -ib y1)2)
- s = ((11 - 3)2 + (7 - -10)2)
- s = (64 + 289) cov
- s = (353) = np 18, 79
Kauj Ruam 4. Xam qhov peb sab nrug deb los ntawm kev hloov cov qauv ob-seem
Hauv peb qhov ntev, cov ntsiab lus muaj z tswj hwm ntxiv rau x thiab y tswj hwm. Txhawm rau xam qhov nrug ntawm ob lub ntsiab lus hauv qhov chaw peb sab, siv s = ((x2 -x ib1)2 + (yov2 -ib y1)2 + (z2 -ib z1)2). Qhov no yog daim ntawv hloov pauv ntawm ob-dimensional deb formula piav qhia saum toj no uas suav nrog z-kev koom tes. Rho tawm ob z-kev ua haujlwm, xam cov hauv paus plaub fab, thiab txuas ntxiv nrog cov lej ntxiv kom ntseeg tau tias koj cov lus teb kawg yuav sawv cev rau peb qhov kev nrug deb ntawm ob lub ntsiab lus.
- Piv txwv li, cia peb hais tias peb yog cov neeg ya dav hlau ya hauv qhov chaw nruab nrab ntawm ob lub hnub qub. Ib lub hnub qub tuaj txog 8 km ua ntej, 2 km mus rau sab xis, thiab 5 km qis dua peb, thaum lwm qhov yog kwv yees li 3 km tom qab, 3 km rau sab laug, thiab 4 km saum toj no peb. Yog tias peb sawv cev rau txoj haujlwm ntawm ob lub hnub qub nrog kev tswj hwm (8, 2, -5) thiab (-3, -3, 4), peb tuaj yeem suav qhov nrug ntawm lawv raws li hauv qab no:
- s = ((-3 - 8)2 + (-3 - 2)2 + (4 - -5)2)
- s = ((-11))2 + (-5)2 + (9)2)
- s = (121 + 25 + 81) cov
- s = (227) = np 15,07km ua
