Yuav Lej Li Cas Ze Li Cas: 8 Kauj Ruam (nrog Duab)

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Yuav Lej Li Cas Ze Li Cas: 8 Kauj Ruam (nrog Duab)
Yuav Lej Li Cas Ze Li Cas: 8 Kauj Ruam (nrog Duab)

Video: Yuav Lej Li Cas Ze Li Cas: 8 Kauj Ruam (nrog Duab)

Video: Yuav Lej Li Cas Ze Li Cas: 8 Kauj Ruam (nrog Duab)
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Qhov nrug, feem ntau muab qhov sib txawv d, yog ntsuas ntawm qhov chaw muaj los ntawm kab ncaj nruab nrab ntawm ob lub ntsiab lus. Kev nrug deb tuaj yeem hais txog qhov chaw nruab nrab ntawm ob lub ntsiab lus nyob ruaj khov (piv txwv li, tus neeg qhov siab yog qhov deb ntawm hauv qab nws txhais taw mus rau saum nws lub taub hau) lossis tuaj yeem hais txog qhov chaw nruab nrab ntawm txoj haujlwm tam sim no khoom thiab nws pib qhov chaw. Feem ntau cov teeb meem nyob deb tuaj yeem daws nrog qhov sib npaug d = osavg × t qhov twg d yog nrug, savg yog qhov nruab nrab nrawm, thiab t yog lub sijhawm, lossis siv d = √ ((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.

Cov kauj ruam

Txoj Kev 1 ntawm 2: Nrhiav Qhov Nruab Nrab Nrog Qhov Nruab Nrab Ceev thiab Sijhawm

Xam Qhov Zaum Kauj Ruam 1
Xam Qhov Zaum Kauj Ruam 1

Kauj Ruam 1. Nrhiav qhov tseem ceeb rau qhov nrawm nruab nrab thiab sijhawm

Thaum koj sim nrhiav qhov deb uas cov khoom txav tau mus, ob daim ntawv xov xwm tseem ceeb heev rau kev suav qhov no: nws ceev (lossis qhov nrawm nrawm) thiab sij hawm tias nws tau txav mus los. Nrog rau cov ntaub ntawv no, nws tuaj yeem nrhiav qhov deb ntawm qhov khoom tau taug kev siv cov qauv d = savg × 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 mus deb npaum li cas ib nrab teev. Siv 120mph ib raws li peb tus nqi rau qhov nruab nrab nrawm thiab 0.5 teev raws li peb tus nqi rau lub sijhawm, peb yuav daws qhov teeb meem no hauv cov kauj ruam tom ntej.

Xam Zaum Kauj Ruam 2
Xam Zaum Kauj Ruam 2

Kauj Ruam 2. Muab qhov nruab nrab nrawm nruab nrab ntawm lub sijhawm

Thaum koj paub qhov nrawm nruab nrab ntawm cov khoom txav mus los thiab lub sijhawm nws tab tom taug kev, nrhiav qhov nrug nws tau mus yog qhov ncaj. Cias muab ob qhov ntau los nrhiav koj cov lus teb.

  • Nco tseg, txawm li cas los xij, yog tias chav nyob ntawm lub sijhawm siv hauv koj tus lej nrawm nrawm sib txawv dua li cov siv hauv koj lub sijhawm, koj yuav tsum hloov pauv ib lossis lwm yam kom lawv sib xws. Piv txwv li, yog tias peb muaj tus nqi nrawm nruab nrab uas tau ntsuas hauv km ib teev thiab tus nqi lub sijhawm uas ntsuas hauv feeb, koj yuav tsum faib tus nqi lub sijhawm los ntawm 60 kom hloov nws mus rau teev.
  • Cia peb daws peb qhov teeb meem piv txwv. 120 mais/teev × 0.5 teev = 60 miv. Nco tseg tias cov koog nyob rau lub sijhawm tus nqi (teev) rho nrog cov koog hauv qhov sib faib ntawm qhov nruab nrab nrawm (teev) kom tawm tsuas yog cov chav nyob nrug deb (mais).
Xam Zaum Kauj Ruam 3
Xam Zaum Kauj Ruam 3

Kauj Ruam 3. Tswj cov kab zauv kom daws tau lwm yam kev hloov pauv

Qhov yooj yim ntawm qhov yooj yim nrug deb (d = savg × t) ua rau nws yooj yim heev rau siv cov kab zauv txhawm rau nrhiav qhov muaj txiaj ntsig ntawm kev hloov pauv ntxiv rau qhov deb. Tsuas yog cais qhov sib txawv uas koj xav daws rau raws li cov cai yooj yim ntawm algebra, tom qab ntawd ntxig qhov tseem ceeb rau koj lwm qhov ob qhov sib txawv kom pom tus nqi thib peb. Hauv lwm lo lus, txhawm rau nrhiav koj lub hom phiaj qhov nruab nrab nrawm, siv qhov sib npaug savg = d/tau thiab txhawm rau nrhiav kom pom lub sijhawm cov khoom tau taug kev, siv qhov sib npaug t = d/savg.

  • Piv txwv li, cia peb hais tias peb paub tias lub tsheb tau tsav 60 mais hauv 50 feeb, tab sis peb tsis muaj tus nqi rau qhov nruab nrab nrawm thaum mus ncig. Hauv qhov no, peb yuav cais tus savg sib txawv hauv qhov yooj yim nrug nrug kom tau savg = d/t, tom qab ntawd tsuas faib 60 mais/50 feeb kom tau txais cov lus teb ntawm 1.2 mais/feeb.
  • Nco ntsoov tias hauv peb qhov piv txwv, peb cov lus teb rau kev nrawm muaj qhov tsis xws luag (mais/feeb). Txhawm rau kom koj cov lus teb nyob rau ntau daim ntawv ntawm mais/teev, sib npaug nws li 60 feeb/teev kom tau txais 72 mais/teev.
Xam Qhov Zaum Kauj Ruam 4
Xam Qhov Zaum Kauj Ruam 4

Kauj Ruam 4. Nco ntsoov tias "savg"sib txawv hauv cov qauv ntsuas nrug yog hais txog qhov nruab nrab nrawm.

Nws yog ib qho tseem ceeb kom nkag siab tias cov lej yooj yim nyob deb muaj qhov pom yooj yim ntawm kev txav ntawm ib yam khoom. Cov qauv nyob deb kwv yees tias cov khoom txav mus los muaj qhov nrawm - hauv lwm lo lus, nws xav tias cov khoom hauv cov lus tsa suab tau txav ntawm ib qho, tsis hloov pauv ntawm qhov nrawm. Txog teeb meem lej lej, xws li cov uas koj tuaj yeem ntsib hauv kev teeb tsa kev kawm, qee zaum nws tseem muaj peev xwm los ua qauv cov khoom siv lub zog siv qhov kev xav no. Hauv lub neej tiag tiag, txawm li cas los xij, tus qauv no feem ntau tsis cuam tshuam qhov kev txav ntawm cov khoom txav, uas tuaj yeem, qhov tseeb, nrawm dua, qeeb, nres, thiab thim rov qab lub sijhawm.

  • Piv txwv li, hauv qhov piv txwv teeb meem saum toj no, peb xaus lus tias yuav mus 60 mais hauv 50 feeb, peb yuav tsum taug kev ntawm 72 mais/teev. Txawm li cas los xij, qhov no tsuas yog qhov tseeb yog tias taug kev ntawm ib qho nrawm rau tag nrho cov kev mus. Piv txwv li, los ntawm kev ncig 80 mais/teev rau ib nrab ntawm kev mus thiab 64 mais/teev rau lwm qhov ib nrab, peb tseem yuav mus 60 mais hauv 50 feeb - 72 mais/teev = 60 mais/50 min = ???? ?
  • Kev suav daws-kev daws teeb meem uas siv cov txiaj ntsig feem ntau yog qhov kev xaiv zoo dua li cov lej nyob deb rau kev txheeb xyuas cov khoom nrawm hauv cov xwm txheej hauv ntiaj teb tiag vim tias muaj kev hloov pauv nrawm dua.

Txoj Kev 2 ntawm 2: Nrhiav Qhov Nruab Nrab Ntawm Ob Lub Ntsiab Lus

Xam Qhov Zaum Kauj Ruam 5
Xam Qhov Zaum Kauj Ruam 5

Kauj Ruam 1. Nrhiav ob lub ntsiab lus spatial coordinates

Yuav ua li cas yog, ntau dua li pom qhov kev ncua deb uas cov khoom txav tau mus, koj yuav tsum nrhiav qhov deb ntawm ob yam khoom nyob ruaj khov? Hauv cov xwm txheej zoo li no, cov qauv ntsuas raws qhov nrawm uas tau piav qhia saum toj no yuav tsis siv. Hmoov zoo, qhov sib cais ntawm tus lej tuaj yeem siv tau yooj yim nrhiav txoj 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 koj ob lub ntsiab lus. Yog tias koj tab tom daws teeb meem ib leeg-nrug deb (xws li ntawm kab lej), koj cov kev tswj hwm yuav yog ob tus lej, x1 thiab x2. Yog tias koj tab tom cuam tshuam nrog kev nrug deb ntawm ob qhov ntev, koj yuav xav tau qhov txiaj ntsig rau ob (x, y) cov ntsiab lus, (x1, y ua1) thiab (x2, y ua2). Thaum kawg, rau peb qhov ntev, koj yuav xav tau qhov tseem ceeb rau (x1, y ua1z, xav1) thiab (x2, y ua2z, xav2).

Xam Qhov Zaum Kauj Ruam 6
Xam Qhov Zaum Kauj Ruam 6

Kauj Ruam 2. Nrhiav 1-D nrug los ntawm kev rho tus nqi ntawm kev sib koom ua ke rau ob lub ntsiab lus

Xam ib seem ntawm qhov nruab nrab ntawm ob lub ntsiab lus thaum koj paub tus nqi rau txhua tus yog qhov raug. Cias siv cov mis d = x2 -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 koj ob lub ntsiab lus dag ntawm tus lej lossis kab.

  • Nco ntsoov tias cov qauv no siv qhov tseem ceeb tshaj plaws (the " | |"cim". Qhov tseem ceeb tsis yog txhais tau tias cov ntsiab lus muaj nyob hauv cov cim ua qhov zoo yog tias lawv tsis zoo.
  • Piv txwv li, cia peb hais tias peb tau nres ntawm ib sab ntawm txoj kev ntawm txoj kev ncaj nraim ntawm txoj kev loj. Yog tias muaj lub nroog me 5 mais ua ntej ntawm peb thiab lub nroog 1 mais qab peb, ob lub nroog sib nrug deb npaum li cas? Yog tias peb teev lub nroog 1 ua x1 = 5 thiab nroog 2 raws li x1 = -1, peb tuaj yeem pom d, qhov deb ntawm ob lub nroog, raws li hauv qab no:

    • d = x2 -x ib1|
    • = |-1 - 5|
    • = |-6| = 6 miv.
Xam Zaum Kauj Ruam 7
Xam Zaum Kauj Ruam 7

Kauj Ruam 3. Nrhiav 2-D nrug los ntawm kev siv Pythagorean theorem

Nrhiav kev nrug deb ntawm ob lub ntsiab lus hauv qhov chaw ob seem yog qhov nyuaj dua li hauv ib qho, tab sis tsis nyuaj. Cias siv cov mis d = √ ((x2 -x ib1)2 + (yov2 -ib y1)2). Hauv cov qauv no, koj rho tawm ob x kev sib koom ua ke, faib cov txiaj ntsig, rho tawm cov y ua haujlwm, square cov txiaj ntsig, tom qab ntawd ntxiv ob qho txiaj ntsig nruab nrab ua ke thiab siv lub hauv paus cag kom pom qhov nrug ntawm koj ob lub ntsiab lus. Cov mis no ua haujlwm hauv ob lub dav hlau dav dav - piv txwv, ntawm cov duab x/y yooj yim.

  • Tus lej 2-D nyob deb siv qhov zoo ntawm Pythagorean theorem, uas hais tias qhov hypotenuse ntawm daim duab peb sab yog sib npaug rau cov hauv paus cag ntawm cov xwm txheej ntawm ob sab.
  • Piv txwv, cia 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 qhov ncaj-kab nrug ntawm ob lub ntsiab lus no, peb tuaj yeem daws raws li hauv qab no:
  • d = √ ((x2 -x ib1)2 + (yov2 -ib y1)2)
  • d = √ ((11 - 3)2 + (7 - -10)2)
  • d = √ (64 + 289)
  • d = √ (353) = 18.79
Xam Zaum Kauj Ruam 8
Xam Zaum Kauj Ruam 8

Kauj Ruam 4. Nrhiav 3-D nrug los ntawm kev hloov kho tus qauv 2-D

Hauv peb qhov loj me, cov ntsiab lus muaj z tswj hwm ntxiv rau lawv cov x thiab y tswj hwm. Txhawm rau nrhiav qhov kev ncua deb ntawm ob lub ntsiab lus hauv qhov chaw peb sab, siv d = √ ((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 siv z tswj hwm rau hauv tus lej. Rho tawm ob z kev sib koom ua ke, ntsuas lawv, thiab ua mus ntxiv los ntawm cov mis ntxiv raws li saum toj no yuav ua kom koj cov lus teb kawg sawv cev rau peb qhov kev nrug deb ntawm koj ob lub ntsiab lus.

  • Piv txwv li, cia peb hais tias peb yog ib tus neeg ya saum nruab ntug nyob hauv qhov chaw ze ob lub hnub qub. Ib qho yog txog 8 kis lus mev ntawm peb, 2 km rau sab xis ntawm peb, thiab 5 mais qis dua peb, thaum lwm qhov yog 3 km qab peb, 3 km rau sab laug ntawm peb, thiab 4 km saum peb. Yog tias peb sawv cev rau txoj haujlwm ntawm cov hnub qub no nrog kev ua haujlwm (8, 2, -5) thiab (-3, -3, 4), peb tuaj yeem pom qhov kev ncua deb ntawm ob qho raws li hauv qab no:
  • d = √ ((- 3 - 8)2 + (-3 - 2)2 + (4 - -5)2)
  • d = √ ((-11)2 + (-5)2 + (9)2)
  • d = √ (121 + 25 + 81)
  • d = √ (227) = np 15.07km ib

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