# Question #2d7d4

Sep 20, 2017

The first vector $\vec{{V}_{1}}$ has a magnitude of 11.7 m and is angled 35.8° counterclockwise from the +x direction.

so $\vec{{V}_{1}} = 11.7 \cos 35.8 \hat{i} + 11.7 \sin 35.8 \hat{j}$

$\implies \vec{{V}_{1}} = 9.5 \hat{i} + 6.8 \hat{j}$

The 2ndt vector $\vec{{V}_{2}}$ has a magnitude of16.5 m and is angled 13.0° counterclockwise from the -x direction.

so $\vec{{V}_{2}} = 16.5 \cos 193 \hat{i} + 16.5 \sin 193 \hat{j}$

$\implies \vec{{V}_{2}} = - 16.0 \hat{i} - 3.7 \hat{j}$

So resultant vector

$\implies \vec{V} = \vec{{V}_{1}} + \vec{{V}_{2}} = - 7.5 \hat{i} + 3.1 \hat{j}$

(a) so magnitude of resultant vector

$\implies \left\mid \vec{V} \right\mid = \left\mid - 7.5 \hat{i} + 3.1 \hat{j} \right\mid = 8.1 m$

(b) And the resultant makes an angle

${\tan}^{-} 1 \left(- \frac{3.1}{7.5}\right) = {157.5}^{\circ}$counter clockwise with +x axis