Question

Find the direction of the dune of these two vectors

Answer 1

Given:

Vector A = 63.5 m at 90 degrees

Vector B = 101 m at 57.0 degrees

Let's find the direction of the sum of these two vectors.

To find the direction, let's first find the x- and y-components of the vectors.

• Vector A:

`\begin{gathered} A_x=65.3cos90=0\text{ m} \\ A_y=63.5sin90=63.5\text{ m} \end{gathered}`

• Vector B:

`\begin{gathered} B_x=101cos57.0=55\text{ m} \\ B_y=101sin57=84.7\text{ m} \end{gathered}`

For the sum of components, we have:

x = Ax + Bx = 0 + 55 = 55 m

y = Ay + By = 63.5 + 84.7 = 148.2 m

Now, to find the direction of the sum, we have:

`\theta=tan^(-1)((y)/(x))`

Plug in the values and solve for θ.

We have:

`\begin{gathered} \theta=tan^(-1)((148.2)/(55)) \\ \\ \theta=69.6^o \end{gathered}`

Therefore, the direction of the sum of the vectors is 69.6 degrees.

ANSWER:

69.6 degrees.