Vector - matambudziko nemhinduro
Vector uye Scalar
1. Pakati pesarudzo dzinotevera, idzo dziri scalar-vector pairs…
A. Simba - kukurumidza
B. Kumanikidzwa - simba
C. Kutamiswa - kumhanya
D. Mhepo yemagetsi - kumanikidzwa
Solution:
Simba = vhekitori, kukurumidza = vector
Kumanikidzwa = scalar, simba = vekitori
Kutamiswa = vhekita, kumhanya = scalar
Magetsi emagetsi = scalar, kumanikidzwa = scalar
Mhinduro chaiyo ndeiyi B.
2.
Mhinduro chaiyo inoratidzwa nenhamba…
A. 1 ne4
B. 1 na2
C. 2 ne3
D. 3 ne4
Solution:
Kumhanya = scalar
Kudzingwa = vekitori
uremu = vekitori
Kukurumidzisa = vekitori
Mhinduro chaiyo ndeinoti C.
Zvikamu zvemavector
3. Maveki maviri, F1 = 20 N uye F2 = 30 N, ratidza gwara sezvakaratidzwa mumufananidzo uri pazasi. Sarudza mhedzisiro yezvikamu zvemavector mu x-axis ne y-axis.
A. 5√3 N uye -25 N
B. -5√3 N uye 25 N
C. 25 N uye 5√3 N
D. 30 N uye 25√3 N
Zvinozivikanwa:
F 1 = 20 Newton
Angle iri pakati peF1 uye x axis = 30o
F 2 = 30 Newton
Angle iri pakati peF2 uye x axis = 30o
Zvaidiwa: Fx uye Fy
Solution:
F1x =F1 kusvika 30o = (20)(0.5√3) = 10√3 MaNewton (pamwe nechiratidzo chekuti chinongedzera ku +x axis)
F1y =F1 pasina 30o = (20)(0.5) = 10 Newtons (pamwe nechiratidzo chekuti chinongedzo ku +y axis)
F2x =F2 kusvika 30o = (30)(0.5√3) = -15√3 Newton (chiratidzo chekubvisa nekuti chinongedzera ku -x axis)
F2y =F2 pasina 30o = (30)(0.5) = 15 Newtons (pamwe nechiratidzo chekuti chinongedzera ku +y axis)
Mhedzisiro yechikamu che x:
Fx =F1x +F2x = 10√3 N – 15√3 N = -5√3 MaNewton
Mhedzisiro yechikamu che y:
Fy =F1y +F2y = 10 N + 15 N = 25 Newton
Mhinduro chaiyo ndeiyi B.
Mhedzisiro yemavector maviri
4. Vana vaviri A naB vakasunda bhokisi, kana A akasunda bhokisi kuenda kumaodzanyemba nesimba re400 N uye panguva imwe chete B akasunda bhokisi kuenda kumabvazuva nesimba re300 N, ipapo tsvaga mhedzisiro yesimba reA naB.
A. 100 N kuchamhembe
B. 100 N kumabvazuva
C. 500 N kuchamhembe kwakadziva kumabvazuva
D. 700 N kuchamhembe kwakadziva kumabvazuva
Zvinozivikanwa:
U = kuchamhembe, T = kumabvazuva, S = kumaodzanyemba, B = kumadokero
TL = kuchamhembe kwakadziva kumabvazuva, TG = kumaodzanyemba kwakadziva kumabvazuva, BD = kumaodzanyemba kwakadziva kumadokero, BL = kuchamhembe kwakadziva kumadokero
A = 400 maNewton kumaodzanyemba
B = 300 maNewton kumabvazuva
Kuda: hukuru uye gwara resimba remambure (R)
Solution:
Mhinduro chaiyo ndeinoti C.
Mhedzisiro yevector yekutama
5.Smumwe munhu ari kutasva bhasikoro kubva kumba 6 km kuenda kuchamhembe ipapo 8 km kumabvazuva. Sarudza nzvimbo yekupedzisira yemunhu kubva panzvimbo yekutanga.
A. 14 km kuchamhembe kwakadziva kumabvazuva
B. 14 km kumaodzanyemba kwakadziva kumadokero
C. 10 km kuchamhembe kwakadziva kumabvazuva
D. 10 km kuchamhembe kwakadziva kumadokero
Zvinozivikanwa:
Kuda: hukuru uye gwara rekutama kunoguma kwaitika
Solution:
Mhinduro chaiyo ndeinoti C.
6.
Zvichibva pamufananidzo uri pamusoro apa, Kana sikweya imwe ichimiririra 1 km, saka chii chinonzi kufamba kwese.
Solution:
Kureba = A + B + C = 6 + 6 + 2 = 14 km
Kutamiswa = R = 12 km
7. Mota inofamba kubva A kuenda kuB ichifamba makiromita makumi matatu kuchamhembe, yozotevera makiromita makumi matanhatu kumabvazuva, yozotevera makiromita zana negumi kumaodzanyemba. Sarudza kuti mota yacho yafamba sei kubva A kuenda kuD.
Solution:
AA' = 60 km
A'D = 110 km - 30 km = 80 km
8. Mota inofamba kubva kuguta A kuenda kuguta B makiromita zana kuchamhembe, yozoenda kuguta C makiromita makumi matanhatu kumabvazuva, yozoenda kuguta D makiromita makumi maviri kumaodzanyemba. Sarudza kuti mota yacho yakafamba sei.
Solution:
D'D = 60 km
AD' = 100 km - 20 km = 80 km
- Chii chinonzi vekitori?
- Pindura: Vector ihuwandu hune hukuru (saizi) uye gwara. Mienzaniso inosanganisira kumhanya, simba, uye kukurumidza.
- Vector yakasiyana sei nescalar?
- Pindura: Scalar ine hukuru chete, nepo vector ine hukuru uye gwara. Semuenzaniso, tembiricha iscalar nekuti ine kukosha asi haina gwara, nepo velocity ivector nekuti inoratidza kumhanya (hukuru) munzira yakati.
- Vector inogona sei kumirirwa nemifananidzo?
- Pindura: Vekitari inogona kumiririrwa nemufananidzo nemuseve. Kureba kwemuseve kunomiririra hukuru hwevekitari, uye divi remuseve rinoratidza divi revekitari.
- Chii chinorehwa nemuswe nemusoro wevector?
- Pindura: Muswe ndiwo panotangira vector, uye musoro (kana kuti muromo) ndiwo panogumira. Pakuita mabasa akadai sekuwedzera vector, muswe weimwe vector unoiswa pamusoro peimwe.
- Mavector anowedzerwa sei pamwe chete?
- Pindura: Mavector anowedzerwa uchishandisa nzira yekubva kumusoro kuenda kumuswe. Muswe wevector yechipiri unoiswa pamusoro peyekutanga. Vector inobuda inotorwa kubva kumuswe wevector yekutanga kuenda kumusoro wevector yechipiri.
- Ndeupi musiyano uripo pakati peyuniti vector ne null vector?
- Pindura: Vekitari yeyuniti ine hukuru hweimwe uye inonongedza munzira yakatarwa. Inoshandiswa kumiririra divi revekitari pasina hanya nehukuru hwayo. Vekitari isina chinhu (kana zero) haina hukuru uye haina divi rakati.
- Vector inogona sei kuwanda ne scalar?
- Pindura: Kuwanda kwevector ne scalar kunochinja hukuru hwayo asi kwete gwara rayo. Kana scalar iri positive, gwara rinoramba rakafanana; kana iri negative, gwara rinodzoserwa shure.
- Zvinorevei kuti mavector maviri ave akatenderera kana kuti akamira?
- Pindura: Mavector maviri akaenzana kana kuti akamira zvakanaka kana kona iri pakati pawo iri 90 degrees. Chigadzirwa chavo chedot chichava zero.
- Mhedzisiro yemavector maviri inoonekwa sei?
- Pindura: Chinobuda ndicho huwandu hwemavector maviri. Pamifananidzo, kana mavector akamiririrwa semiseve, unogona kuwana chinobuda nekuisa muswe wevector yechipiri pamusoro peyekutanga wodhirowa museve mutsva (unobuda) kubva kumuswe wevector yekutanga kuenda kumusoro weyechipiri.
- Kana vhekitari ikananga kumabvazuva ine hukuru hwemayuniti gumi, ungatsanangura sei zvakapesana nazvo?
- Pindura: Zvakapesana neiyi vhekitari zvaizova nehukuru hwakafanana (mayuniti gumi) asi zvaizonongedzera kune rimwe divi rakapesana, kureva, kumadokero.
