Question

Find the magnitude of the sum

Answer 1

Answer:

$\displaystyle |\vec{v_1}+\vec{v_2}|=4.15m$

Explanation:

Sum of Vectors in the Plane

Given two vectors

$\displaystyle \vec{v_1}\ ,\ \vec{v_2}$

They can be expressed in their rectangular components as

$\displaystyle \vec{v_1}=$

$\displaystyle \vec{v_2}=$

The sum of both vectors can be done by adding individually its components

$\displaystyle \vec{v_1}+\vec{v_2}=$

If the vectors are given as a magnitude and an angle $(M\ ,\ \theta )$, each component can be found as

$\displaystyle \vec{v_1}=$

$\displaystyle \vec{v_2}=$

The first vector has a magnitude of 3.14 m and an angle of 30°, so

$\displaystyle \vec{v_1}=$

$\displaystyle \vec{v_1}=$

The second vector has a magnitude of 2.71 m and an angle of -60°, so

$\displaystyle \vec{v_2}=$

$\displaystyle \vec{v_2}=$

The sum of the vectors is

$\displaystyle \vec{v_1}+\vec{v_2}=$

$\displaystyle \vec{v_1}-\vec{v_2}=$

Finally, we compute the magnitude of the sum

$\displaystyle |\vec{v_1}+\vec{v_2}|=\sqrt{(4.08)^2+(-0.78)^2}$

$\displaystyle |\vec{v_1}+\vec{v_2}|=\sqrt{17.25}$

$\displaystyle |\vec{v_1}+\vec{v_2}|=4.15m$