Respuesta :
ANSWER:
46.1 miles/hr
STEP-BY-STEP EXPLANATION:
We calculate the x and y coordinates of each vector just like this:
For the plane:
[tex]\begin{gathered} P_x=70\cdot\cos24\degree=63.948\text{ mph} \\ \\ P_y=70\cdot\sin24\degree=28.472\text{ mph} \end{gathered}[/tex]For the wind:
[tex]\begin{gathered} W_x=25\cdot\:\cos190\degree=-24.620\text{ mph} \\ \\ W_y=25\cdot\:\sin190\degree=-4.341\text{ mph} \end{gathered}[/tex]We calculate the resulting vector:
[tex]\begin{gathered} V_x=63.948-24.620=39.328\text{ mph} \\ \\ V_y=28.472-4.341=24.131\text{ mph} \end{gathered}[/tex]Now, we calculate the norm of the vector as follows:
[tex]\begin{gathered} V=\sqrt{(V_x)^2+(V_y)^2} \\ \\ V=\sqrt{\left(39.328\right)^2+\left(24.131\right)^2} \\ \\ V=\sqrt{2128.99} \\ \\ V=46.1\text{ mph} \end{gathered}[/tex]The speed of the plane is 46.1 miles per hour.
