Question

Seja uma força F with rightwards arrow on top inclinada de um ângulo alpha em relação ao eixo horizontal (eixo x) e inclinado de um ângulo beta em relação ao eixo vertical (eixo y). Uma vez que força é uma grandeza vetorial, representada por vetor, podemos utilizar o plano cartesiano para descrevê-la algebricamente, sendo stack F subscript x with rightwards arrow on top equals open vertical bar stack F subscript x with rightwards arrow on top close vertical bar space i with hat on top a componente ou projeção horizontal de (no eixo x) e stack F subscript y with rightwards arrow on top equals open vertical bar stack F subscript y with rightwards arrow on top close vertical bar stack space j with hat on top a componente ou projeção vertical de (no eixo y). Assim, o vetor F with rightwards arrow on top pode ser decomposto nas suas projeções stack F subscript x with rightwards arrow on top e stack F subscript y with rightwards arrow on top, sendo os módulos dessas projeções dados, respectivamente, por: open vertical bar stack F subscript x with rightwards arrow on top close vertical bar equals F times cos alpha equals F times s e n beta e open vertical bar stack F subscript y with rightwards arrow on top close vertical bar equals F times cos beta equals F times s e n alpha . E podemos representar o vetor inclinado através das suas projeções, ou seja: F with rightwards arrow on top equals open vertical bar stack F subscript x with rightwards arrow on top close vertical bar stack space i with hat on top space plus space open vertical bar stack F subscript y with rightwards arrow on top close vertical bar stack space j with hat on top .
Considere a figura a seguir que mostra vetores no plano cartesiano:

Figura
Fonte: A autora.

Considere os módulos dos vetores A with rightwards arrow on top, B with rightwards arrow on top , e C with rightwards arrow on top indicados na figura acima, respectivamente iguais a 12, 15 e 6 em unidades arbitrárias.
Assinale a alternativa que contém correta e respectivamente a projeção horizontal do vetor A with rightwards arrow on top, a projeção vertical do vetor B with rightwards arrow on top e a projeção horizontal do vetor C with rightwards arrow on top, indicados na figura acima.
Escolha uma:
a.
stack A subscript x with rightwards arrow on top equals negative 12 times cos left parenthesis 37 º right parenthesis stack space i with hat on top space semicolon space stack B subscript y with rightwards arrow on top equals 15 times cos left parenthesis 40 º right parenthesis stack space j with hat on top space semicolon space stack C subscript x with rightwards arrow on top equals negative 6 times cos left parenthesis 60 º right parenthesis stack space i with hat on top space semicolon space space
b.
stack A subscript x with rightwards arrow on top equals 12 times cos left parenthesis 37 º right parenthesis stack space i with hat on top space semicolon space stack B subscript y with rightwards arrow on top equals negative 15 times cos left parenthesis 40 º right parenthesis stack space j with hat on top space semicolon space stack C subscript x with rightwards arrow on top equals 6 times cos left parenthesis 60 º right parenthesis stack space i with hat on top space semicolon space space
c.
stack A subscript x with rightwards arrow on top equals 12 times s e n left parenthesis 37 º right parenthesis stack space i with hat on top space semicolon space stack B subscript y with rightwards arrow on top equals negative 15 times s e n left parenthesis 40 º right parenthesis stack space j with hat on top space semicolon space stack C subscript x with rightwards arrow on top equals 6 times cos left parenthesis 60 º right parenthesis stack space i with hat on top space semicolon space space
d.
stack A subscript x with rightwards arrow on top equals 12 times s e n left parenthesis 37 º right parenthesis stack space i with hat on top space semicolon space stack B subscript y with rightwards arrow on top equals negative 15 times s e n left parenthesis 40 º right parenthesis stack space j with hat on top space semicolon space stack C subscript x with rightwards arrow on top equals negative 6 times cos left parenthesis 60 º right parenthesis stack space i with hat on top space semicolon space space
e.
stack A subscript x with rightwards arrow on top equals 12 times s e n left parenthesis 37 º right parenthesis stack space i with hat on top space semicolon space stack B subscript y with rightwards arrow on top equals negative 15 times s e n left parenthesis 40 º right parenthesis stack space j with hat on top space semicolon space stack C subscript x with rightwards arrow on top equals negative 6 times s e n left parenthesis 60 º right parenthesis stack space i with hat on top space semicolon space space

Answer 1

Resposta:

Explicação: CORRIGIDO PELO AVA