The discussion focuses on solving a vector word problem involving an airplane flying on a bearing of South 27 degrees West at 485 mph, with a wind blowing from South 72 degrees East at 35 mph. The velocity vectors for the airplane and wind are defined as v = 485⟨cos(117°), -sin(117°)⟩ and w = 35⟨cos(162°), sin(162°)⟩, respectively. The resultant ground speed vector is calculated using the vector sum r = v + w. The angles 117 degrees and 162 degrees are derived from the bearings provided in the problem.
Students in physics or engineering, pilots, navigators, and anyone interested in solving vector problems related to motion and wind effects.
MarkFL said:Hello, and welcome to MHB, Gummg! (Wave)
I would write the plane's velocity vector as:
$$\vec{v}=485\left\langle \cos\left(117^{\circ}\right),-\sin\left(117^{\circ}\right) \right\rangle$$
And the wind's velocity vector as:
$$\vec{w}=35\left\langle \cos\left(162^{\circ}\right),\sin\left(162^{\circ}\right) \right\rangle$$
And so the resultant ground speed vector will be the vector sum:
$$\vec{r}=\vec{v}+\vec{w}$$
Can you proceed?
Gummg said:How did you get 117 and 162 degrees?