Question

Consider the vector b⃗ with magnitude 4.00 m at an angle 23.5∘ north of east. what is the x component bx of this vector?

Answer 1

Answer:

3.67 m

Explanation:

A physical quantity is said to be vector quantity if it need a magnitude as well as direction for complete explanation.

It makes an angle 23.5 degree from positive X axis.

So, it's component along X axis is given by

bx = B Cos theta

bx = 4 × Cos 23.5

bx = 3.67 m

Answer 2

The magnitude of the x-component of the vector $\vec b$ is $\boxed{3.667\,\text{m}}$.

Further Explanation:

Given:

The magnitude of the vector $\vec b$ is $4\,\text{m}$.

The angle made by the vector with the horizontal is $23.5^\circ$.

Concept:

A vector is a quantity that requires the magnitude as well as the direction for the complete representation of the unit whereas the quantity that requires only the magnitude for its representation is termed as the scalar quantity.

If a vector makes an angle of $\theta$ with the horizontal, then the x-component or the horizontal component of the vector is given by.

 ${\vec b_x} = b\cos \theta$

Substitute $4\,{\text{m}}$ for $b$ and $23.5^\circ$ for $\theta$ in above expression.

$\begin{aligned}{{\vec b}_x} &= 4\cos \left( {23.5^\circ } \right)\\&= 4 \times 0.917 \\&\approx 3.67\,{\text{m}}\\\end{aligned}$

Thus, the x-component of the vector $\vec b$ is $\boxed{3.67\,{\text{m}}}$.

Learn More:

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Answer Details:

Grade: High School

Chapter: Vectors and Scalars

Subject: Physics

Keywords:  Vector, scalar, magnitude, direction, component, direction, bx, the x-component, quantity, physical, only magnitude.