Roboguru

Dua vektor gaya F1​​ dan F2​​ bertitik tangkap sama dan saling mengapit sudut α. Jika ∣∣​F1​+F2​∣∣​=3​∣∣​F1​−F2​∣∣​ dan F1​=F2​=F nilai sebesar...

Pertanyaan

Dua vektor gaya begin mathsize 14px style stack F subscript 1 with rightwards arrow on top end style dan begin mathsize 14px style stack F subscript 2 with rightwards arrow on top end style bertitik tangkap sama dan saling mengapit sudut begin mathsize 14px style alpha end style. Jika begin mathsize 14px style open vertical bar F with rightwards arrow on top subscript 1 plus F with rightwards arrow on top subscript 2 close vertical bar equals square root of 3 open vertical bar F with rightwards arrow on top subscript 1 minus F with rightwards arrow on top subscript 2 close vertical bar end style dan begin mathsize 14px style F subscript 1 equals F subscript 2 equals F end style nilai begin mathsize 14px style alpha end style sebesar...space

  1. begin mathsize 14px style 30 to the power of straight omicron end style space

  2. undefined space

  3. begin mathsize 14px style 60 to the power of straight omicron end style space

  4. begin mathsize 14px style 90 to the power of straight omicron end style space

  5. begin mathsize 14px style 180 to the power of straight omicron end style 

Pembahasan Video:

Pembahasan Soal:

Diketahui:

begin mathsize 14px style F subscript 1 equals F subscript 2 equals F end style 

begin mathsize 14px style open vertical bar F subscript 1 plus F subscript 2 close vertical bar equals square root of 3 open vertical bar F subscript 1 minus F subscript 2 close vertical bar end style 

Ditanya: begin mathsize 14px style alpha end style ?

Pembahasan:

- Besar jumlah 2 vektor

begin mathsize 14px style open vertical bar F subscript 1 plus F subscript 2 close vertical bar squared equals F subscript 1 squared plus F subscript 2 squared plus 2 F subscript 1 F subscript 2 space cos space alpha end style  

- Besar selisih 2 vektor

begin mathsize 14px style vertical line F subscript 1 minus F subscript 2 vertical line end style to the power of size 14px 2 size 14px equals size 14px F subscript size 14px 1 to the power of size 14px 2 size 14px plus size 14px F subscript size 14px 2 to the power of size 14px 2 size 14px minus size 14px space size 14px 2 size 14px F subscript size 14px 1 size 14px F subscript size 14px 2 size 14px space size 14px cos size 14px space size 14px alpha 

maka, 

=> Error converting from MathML to accessible text. 

=> size 14px F subscript size 14px 1 to the power of size 14px 2 size 14px plus size 14px F subscript size 14px 2 to the power of size 14px 2 size 14px plus size 14px space size 14px 2 size 14px F subscript size 14px 1 size 14px F subscript size 14px 2 size 14px space size 14px cos size 14px space size 14px alpha size 14px space size 14px equals size 14px space size 14px 3 size 14px space size 14px left parenthesis size 14px F subscript size 14px 1 to the power of size 14px 2 size 14px plus size 14px F subscript size 14px 2 to the power of size 14px 2 size 14px minus size 14px space size 14px 2 size 14px F subscript size 14px 1 size 14px F subscript size 14px 2 size 14px space size 14px cos size 14px space size 14px alpha size 14px right parenthesis 

=> undefined 

=> undefined 

=> size 14px 2 size 14px F to the power of size 14px 2 size 14px plus size 14px space size 14px 2 size 14px F to the power of size 14px 2 size 14px space size 14px cos size 14px space size 14px alpha size 14px space size 14px equals size 14px 6 size 14px F to the power of size 14px 2 size 14px minus size 14px space size 14px 6 size 14px F to the power of size 14px 2 size 14px space size 14px cos size 14px space size 14px alpha 

=> size 14px 8 size 14px F to the power of size 14px 2 size 14px space size 14px cos size 14px space size 14px alpha size 14px space size 14px equals size 14px 4 size 14px F to the power of size 14px 2 

=> begin mathsize 14px style cos space alpha space equals space 1 half end style 

=> begin mathsize 14px style alpha space equals space 60 to the power of o end style 

Oleh karena itu, jawabannya adalah Cspace

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

U. Amalia

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Terakhir diupdate 07 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui vektor a=6satuan, b=8satuan, dan a+b=10satuan. Tentukan besar sudut yang diapit vektor a dan b!

Pembahasan Soal:

begin mathsize 14px style R equals square root of 6 squared plus 8 squared plus 2 left parenthesis 6 right parenthesis left parenthesis 8 right parenthesis space cos space straight theta end root 10 squared equals 36 plus 64 plus 96 space cos space straight theta 100 equals 100 plus 96 space cos space straight theta 96 space cos space straight theta equals 100 minus 100 96 space cos space straight theta equals 0 cos space straight theta equals 0 straight theta equals 90 to the power of straight omicron end style 

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Diketahui vektor ∣∣​u∣∣​=10satuan dan ∣∣​v∣∣​=15satuan. Adapun ∣∣​u+v∣∣​=25satuan. Tentukan sudut apit kedua vektor tersebut!

Pembahasan Soal:

begin mathsize 14px style R equals square root of u with rightwards arrow on top squared plus v with rightwards arrow on top squared plus 2 u with rightwards arrow on top v with rightwards arrow on top space cos space alpha end root open vertical bar u with rightwards arrow on top plus v with rightwards arrow on top close vertical bar equals square root of u with rightwards arrow on top squared plus v with rightwards arrow on top squared plus 2 u with rightwards arrow on top v with rightwards arrow on top space cos space alpha end root 25 equals square root of 10 squared plus 15 squared plus 2 left parenthesis 10 right parenthesis left parenthesis 15 right parenthesis space cos space alpha end root 625 equals 100 plus 225 plus 300 space cos space alpha 300 space cos space alpha equals 300 cos space alpha equals 1 alpha equals 0 to the power of straight omicron end style  

Jadi, sudut apit kedua vektor adalah begin mathsize 14px style 0 to the power of straight omicron end style 

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Roboguru

Kapal yang berlayar di kanal ditarik dengan dua gaya dari sisi kiri dan kanan. Setiap gaya sebesar 1200 N. Kedua gaya membentuk sudut 45o terhadap arah mendatar. Nilai komponen vektor pada arah sumbu ...

Pembahasan Soal:

begin mathsize 14px style F with rightwards arrow on top subscript 1 x end subscript equals 1200 cos 45 degree F with rightwards arrow on top subscript 1 x end subscript equals 1200 cross times 1 half square root of 2 F with rightwards arrow on top subscript 1 x end subscript equals 600 square root of 2 F with rightwards arrow on top subscript 2 x end subscript equals 1200 cos 45 degree F with rightwards arrow on top subscript 2 x end subscript equals 1200 cross times 1 half square root of 2 F with rightwards arrow on top subscript 2 x end subscript equals 600 square root of 2 end style 

Gaya yang berpengaruh di sisi kiri kapal adalah begin mathsize 14px style F with rightwards arrow on top subscript 1 x end subscript equals 600 square root of 2 end style N

Jadi, jawaban yang tepat adalah B.

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Roboguru

Perhatikan posisi titik pada koordinat cartesius berikut!   Jika 1 kotak mewakili 0,5 meter, nyatakan posisi titik dalam vektor satuan, besar dan arahnya r adalah...

Pembahasan Soal:

Diketahui : 

x equals 3 space kotak cross times 0 comma 5 space equals 1 comma 5 space straight m y equals 2 space kotak cross times 0 comma 5 equals 1 space straight m 

Ditanya : besar dan arah vektor r ?

Jawab :

Sudut yang dibentuk oleh sumbu x negatif  dan sumbu y negatif adalah 90°, maka cos space 90 degree equals 0, maka besar vektor r dapat dicari dengan persamaan berikut.

r equals square root of x squared plus y squared end root r equals square root of 1 comma 5 squared plus 1 squared end root r equals square root of 2 comma 25 plus 1 end root r equals square root of 3 comma 25 end root space straight m 

Untuk menentukan arahnya, kita cari terlebih dahulu sudut vektor r terhadap sumbu x negatif

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space alpha end cell equals cell y over x end cell row cell tan space alpha end cell equals cell fraction numerator 1 over denominator 1 comma 5 end fraction end cell row alpha equals cell 33 comma 69 degree end cell end table 

Maka arahnya

theta equals 180 degree plus 33 comma 69 degree theta equals 213 comma 69 degree 

Besar dan arah vektor r adalah square root of 3 comma 25 end root space straight m dan 213,69°.

Jadi, jawaban yang benar adalah B.

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Roboguru

Perhatikan dua vektor berikut!   Uraikan vektor u dan v, lalu tuliskan vektor satuannya!

Pembahasan Soal:

uraian vektor begin mathsize 14px style u with rightwards arrow on top end style:

begin mathsize 14px style u with rightwards arrow on top subscript x equals u space cos space 30 to the power of straight omicron u with rightwards arrow on top subscript x equals 12 left parenthesis 1 half square root of 3 right parenthesis u with rightwards arrow on top subscript x equals 6 square root of 3 space straight N end style 

begin mathsize 14px style u with rightwards arrow on top subscript y equals u space sin space 30 to the power of straight omicron u with rightwards arrow on top subscript y equals 12 left parenthesis 1 half right parenthesis u with rightwards arrow on top subscript y equals 6 space straight N end style  

karena arah vektor begin mathsize 14px style u with rightwards arrow on top subscript x end style ke kiri, maka begin mathsize 14px style u with rightwards arrow on top subscript x end style bernilai negatif. sehingga vektor undefined:

begin mathsize 14px style u with rightwards arrow on top equals open parentheses negative 6 square root of 3 close parentheses i with hat on top plus 6 j with hat on top end style  

 

sedangkan uraian vektor begin mathsize 14px style v with rightwards arrow on top end style:

begin mathsize 14px style v with rightwards arrow on top subscript x equals v space cos space 45 to the power of straight omicron v with rightwards arrow on top subscript x equals 16 left parenthesis 1 half square root of 2 right parenthesis v with rightwards arrow on top subscript x equals 8 square root of 2 space straight N end style 

begin mathsize 14px style v with rightwards arrow on top subscript y equals v space sin space 45 to the power of straight omicron v with rightwards arrow on top subscript y equals 16 left parenthesis 1 half square root of 2 right parenthesis v with rightwards arrow on top subscript y equals 8 square root of 2 space straight N end style  

maka vektor satuannya adalah:

begin mathsize 14px style v with rightwards arrow on top equals left parenthesis 8 square root of 2 right parenthesis i with hat on top plus left parenthesis 8 square root of 2 right parenthesis j with hat on top end style  

 

1

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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