Question

A velocity vector has components 30 meters per second, westward and 25 meters per second northward, what are the magnitude and direction of this vector

Answer 1

Substitute the values:

`\[ \tan(\theta) = (25)/(-30) \]`

`\[ \theta \approx \tan^(-1)\left((25)/(-30)\right) \]`

`\[ \theta \approx \tan^(-1)(-0.8333) \]`

`\[ \theta \approx -39.81^\circ \]`

The direction is approximately
`\(39.81^\circ\)` south of west.

So, the velocity vector has a magnitude of approximately
`\(39.05 \, \text{m/s}\)` and is directed approximately
`\(39.81^\circ\)` south of west.