Question

Find the direction of the sun of these two vectors

Answer 1

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

Step-by-step 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)((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)((87.5)/(135.5))=\tan^(-1)(0.6458) \\ \theta=32.9\degree \end{gathered}`

That is the answer.