Question

Find the x-component of this

vector:
73.3°
12.0 m
Remember, angles are measured from
the +x axis.
x-component (m)

Answer 1

3.45 m

Step-by-step explanation:

You want the x-component of the vector 12.0 m at 73.3°.

Components

The Cartesian coordinates of a point given in polar form can be found from ...

a∠θ = a(cos(θ), sin(θ))

This means the components of the given vector are ...

12.0∠73.3° = 12.0(cos(73.3°), sin(73.3°)) ≈ (3.448, 11.494)

The x-component is about 3.45 m.

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Additional comment

The vector values are given to 3 significant figures, so we have rounded the answer to 3 significant figures. The attached calculator display shows the value to full calculator precision, so you can round it as you may need.

<95141404393>

Answer 2

3.4

Step-by-step explanation:

A two-dimensional vector is defined as:

`\displaystyle{\vec v = a\hat i+b\hat j}`

This forms a horizontal length with magnitude |a| and a vertical length with magnitude |b|. Therefore:

`\displaystyleb=\\ \displaystyle\cos \theta`

a-term is considered as x-component because it forms a horizontal side which is x-axis. The magnitude of vector is given to be 12 meters and the measurement is 73.3°. Therefore, substitute in:

`\displaystyle{a=12\cos 73.3^(\circ)}\\\\\displaystyle{a\approx 3.4}`

Therefore, x-component approximately is 3.4