The discussion revolves around solving a vector word problem involving an airplane's flight path and the influence of wind on its trajectory. Participants are exploring the mathematical representation of the airplane's and wind's velocity vectors to determine the actual bearing and ground speed of the airplane.
There is no consensus on the angles used in the velocity vectors, as one participant seeks clarification on their derivation. The discussion remains unresolved regarding the correctness of the angles and the subsequent calculations.
Participants have not provided explicit definitions for the angles used in the vector representations, and there may be assumptions regarding the coordinate system employed that are not stated.
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?