Question

A car travels 10 km southeast andthen 15 km in a direction 60° north ofeast. Find the direction of the car'sresultant vector.

Answer 1

We need to find the angle x, so let's find the angle of the first two vectors:

`\theta_1=(270+360)/(2)=315`
`\theta_2=60`

so:

`v_x=10cos(315)+15cos(60)=14.57`
`v_y=10sin(315)+15sin(60)=5.91`

Therefore, the angle is:

`\begin{gathered} \theta_r=tan^(-1)((v_y)/(v_x))=tan^(-1)((5.91)/(14.57)) \\ \theta_r=22.11^(\circ) \end{gathered}`

Answer:

The direction of the car's resultant vector is 22.11⁰