Question

a vector of magnitude 10 unit makes an angle 30° with x-axis. find its horizontal and vertical components​

Answer 1

Vector makes an angle of 30° with the x-axis and we are asked to find its vertical and horizontal components

Let the vector be $\sf\overrightarrow{A}$

Calculating Horizontal Component:-

let it's horizontal component be $\sf A_{x}$

$\\ \quad \rightarrow \quad\sf A_{x} = A \cos \theta$

$\\ \quad \rightarrow \quad\sf A_{x} = 1 0 \cos {30}^{0}$

$\\ \quad \rightarrow \quad\sf A_{x} = 1 0 \times \frac{ \sqrt{3} }{2}$

$\\ \quad \therefore \quad \boxed{\sf A_{x} = 5 \sqrt{2} \: units} \bigstar$

Calculating Vertical Component:-

let it's vertical component be $\sf A_{y}$

$\\ \quad \rightarrow \quad\sf A_{y} = A\sin \theta$

$\\ \quad \rightarrow \quad\sf A_{y} = 10\sin {30}^{0}$

$\\ \quad \rightarrow \quad\sf A_{y} = 10 \times \frac{1}{2}$

$\\ \quad \therefore \quad \boxed{\sf A_{y} = 5 \: units} \bigstar$

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