Question

A vector u has a magnitude of 15 and a direction of 0 degrees. A vector v has a magnitude of 9 and a direction of 35 degrees. Find the direction and magnitude of u+v to the nearest whole values

Answer 1

Answer:

$\displaystyle \alpha \simeq 13^o$

$\displaystyle \left | \vec{u}+\bar{v} \right |\simeq 23$

Step-by-step explanation:

Sum Of Vectors

Given

$\displaystyle \vec{u}=, \vec{v}=$

the sum of both is

$\displaystyle \vec{u}+\vec{u}=$

Given a vector

$\displaystyle \vec{x}=$

The magnitude of \vec x is

$\displaystyle \left | \vec{x} \right |=\sqrt{m^2+n^2}$

And the angle is forms with the positive x-axis is

$\displaystyle tan\alpha =\frac{n}{m}$

We have

$\displaystyle \vec{u}=$

$\displaystyle \vec{u}=$

Also

$\displaystyle \vec{v}=$

$\displaystyle \vec{v}=< 7.372,5.162>$

The sum of both vectors is

$\displaystyle \vec{u}+\vec{v}=$

$\displaystyle \vec{u}+\vec{v}=$

The magnitude of the sum is

$\displaystyle \left | \vec{u}+\vec{v} \right |=\sqrt{22.732^2+5.162^2}=22.96$

We compute the angle (direction)

$\displaystyle tan\alpha =\frac{5.162}{22.732}=0.227$

$\displaystyle \alpha =12.79^o$

Rounding to the nearest integer

$\displaystyle \alpha \simeq 13^o$

Rounding the magnitude

$\displaystyle \left | \vec{u}+\bar{v} \right |\simeq 23$