Question

Choose the correct speed and direction of a plane with a velocity of <5, -12>

Answer 1

The speed is the magnitude of the vector given by:

`v=\sqrt[]{v^2_x+v^2_y_{}}_{}`

Plugging the components of the vector we have:

`\begin{gathered} v=\sqrt[]{(5)^2+(-12)^2} \\ v=\sqrt[]{25+144} \\ v=\sqrt[]{169} \\ v=13 \end{gathered}`

Now to find the direction we need to notice that the vector lies on the second quadrant of the coordinate plane, this means that the formula:

`\theta=\tan ^(-1)((v_y)/(v_x))`

does not give the angle we are looking for but the supplementary angle.

Then the direction is given as:

`180-\tan ^(-1)((v_y)/(v_x))`

Plugging the values given we have:

`180-\tan ^(-1)((12)/(5))=113`

Therefore the spped of the plane is 13 and the direction is 113°