Question

find the direction of the sun of these two vectors

Answer 1

ANSWER

$\begin{equation*} 32.9\degree \end{equation*}$

EXPLANATION

First, we have to express the vectors in their component forms.

For the vector with a length of 101 m:

$\begin{gathered} A=(101\cos60)i+(101\sin60)j \\ A=50.5i+87.5j \end{gathered}$

For the vector with a length of 85.0 m:

$\begin{gathered} B=(85\cos0)i+(85\sin0)j \\ B=85i \end{gathered}$

Hence, the sum of the two vectors is:

$\begin{gathered} C=A+B \\ C=50.5i+87.5j+85i \\ C=135.5i+87.5j \end{gathered}$

To find the direction of the sum of the vectors, apply the formula:

$\theta=\tan^{-1}(\frac{y}{x})$

where x = horizontal component of the sum

y = vertical component of the sum

Therefore, the direction of the sum of the vectors is:

$\begin{gathered} \theta=\tan^{-1}(\frac{87.5}{135.5})=\tan^{-1}(0.6458) \\ \theta=32.9\degree \end{gathered}$

That is the answer.