Question

A vector of 10N makes an angle of 30 with positive X-axis. Find its components along X axis and y axis?

Answer 1

Answer:

Given:

A vector of magnitude 10 N is provided.

It is at an angle of 30° to the + x axis.

To find:

The components along the x and y axis.

Calculation:

Along x axis:

F(x) = F cos(θ)

=> F(x) = 10 × cos(30)

=> F(x) = 10 (√3/2) = 5√3N

Along y axis:

F(y) = F sin(θ)

=> F(y) = 10 sin(30°)

=> F(y) = 10 × ½

=> F(y) = 5 N.

Additional information:

1. A vector is a quantity that can be defined with both magnitude and direction.

2. Since force is a vector, we are able to break it down into components along chosen axis.

Answer 2

$\huge{\orange{\underline{\red{\mathbb{GIVEN:-}}}}}$

1.A vector of 10N makes an angle of 30 with positive X-axis.

2.cos30°=√3/2.

3.F=30N.

4.sin30°=1/2.

$\huge{\orange{\underline{\red{\mathbb{FIND:-}}}}}$

X-AXIS COMPONENTS.

Y-AXIS COMPONENTS.

$\huge{\orange{\underline{\red{\mathbb{ANSWER:-}}}}}$

CASE. I)

$\huge\bold\red\rightarrow$f(x)=f cos$\theta$ [FORMULA]

$\huge\bold\red\rightarrow$f(x)=f cos(30°)

$\huge\bold\red\rightarrow$$f(x) = 10 \times \frac{ \sqrt{3} }{2} \\ f(x) = 5 \sqrt{3} n.$

CASE. II)

Y-AXIS.

$\huge\bold\red\rightarrow$F(x)=f sin $\theta$ [FORMULA]

$\huge\bold\red\rightarrow$f(x)=f sin(30°)

$\huge\bold\red\rightarrow$ f(x) = 10 × (1/2)

$\huge\bold\red\rightarrow$f(x)=5N.

$\huge{\orange{\underline{\red{\mathbb{THANKS.}}}}}$