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

Answer:

3.4

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:

$\displaystyle{b=|\vec v|\sin \theta}\\ \displaystyle{a=|\vec v|\cos \theta}$

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