Question

Force of 10n acts at an angle of 30° with horizontal, then it's rectangular components are ______ and ______​

Answer 1

Answer- The above question is from the chapter 'Motion in a Plane'.

Concept used: Resolution of vectors- It is a process of splitting a vector into two components i.e. horizontal component and vertical component.

Horizontal component (aₓ) = a cos θ

Vertical component ( $a_{y}$ ) = a sin θ

Given question: Force of 10 N acts at an angle of 30° with horizontal, then it's rectangular components are ______ and ______​ .

Answer: Let the force by represented by $\vec{F}$ .

$\vec{F}$ = 10 N

θ = 30°

Vertical component ( $F_{y}$ ) = F sin θ

Vertical component ( $F_{y}$ ) = 10 × sin 30°

Vertical component ( $F_{y}$ ) = 10 × $\frac{1}{2}$

Vertical component ( $F_{y}$ ) = 5 N

Horizontal component ( $F_{x}$ ) = F cos θ

Horizontal component ( $F_{x}$ ) = 10 × cos 30°

Horizontal component ( $F_{x}$ ) = 10 × $\frac{\sqrt{3}}{2}$

Horizontal component ( $F_{x}$ ) = 5√3 N

∴ Force of 10 N acts at an angle of 30° with horizontal, then it's rectangular components are 5 N and 5√3 N.

Answer 2

Answer- The above question is from the chapter 'Motion in a Plane'.

Concept used: Resolution of vectors- It is a process of splitting a vector into two components i.e. horizontal component and vertical component.

Horizontal component (aₓ) = a cos θ

Vertical component ( a_{y}a

y

) = a sin θ

Given question: Force of 10 N acts at an angle of 30° with horizontal, then it's rectangular components are ______ and ______ .

Answer: Let the force by represented by \vec{F}

F

.

\vec{F}

F

= 10 N

θ = 30°

Vertical component ( F_{y}F

y

) = F sin θ

Vertical component ( F_{y}F

y

) = 10 × sin 30°

Vertical component ( F_{y}F

y

) = 10 × \frac{1}{2}

2

1

Vertical component ( F_{y}F

y

) = 5 N

Horizontal component ( F_{x}F

x

) = F cos θ

Horizontal component ( F_{x}F

x

) = 10 × cos 30°

Horizontal component ( F_{x}F

x

) = 10 × \frac{\sqrt{3}}{2}

2

3

Horizontal component ( F_{x}F

x

) = 5√3 N

∴ Force of 10 N acts at an angle of 30° with horizontal, then it's rectangular components are 5 N and 5√3 N.