Question

Physics (simple trig): a novice pilot sets a plane's controls, thinking that the plane will fly 250 km/hr to the north. If the wind blows at 75 km/hr to the south east (135 degrees), what is the plane's resultant velocity?

Answer 1

you add the vectors.



add the components individually.

the resulting velocity in the x direction is:

0 + 75cos(-45) = 53.03

in y direction:

250 + 75sin(-45) = 196.97

final = [53.03, 196.97]

\[Magnitude = \left| {\sqrt{(53.03)^2 + (196.97)^2}} \right|\]
\[Angle = \tan^{-1}\left( \frac{ 196.97 }{ 53.03 } \right)\]