MohanadN552669 MohanadN552669
  • 26-10-2022
  • Mathematics
contestada

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

Respuesta :

XyleeB756341 XyleeB756341
  • 26-10-2022

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

[tex]\theta_1=\frac{270+360}{2}=315[/tex][tex]\theta_2=60[/tex]

so:

[tex]v_x=10cos(315)+15cos(60)=14.57[/tex][tex]v_y=10sin(315)+15sin(60)=5.91[/tex]

Therefore, the angle is:

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

Answer:

The direction of the car's resultant vector is 22.11⁰

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