Airplane vector problem - wind due east, plane northeast; need help drawing a picture A wind is blowing straight east with a velocity of 25 mph and an aircraft is flying pointed North East (.e., at a $45^{\circ}$ if the $y$-axis points north and the $x$-axis points east) and records an airspeed of $130$ mph. I need to determine in which direction and how fast the airplane is actually traveling. Numerically, I can figure this out, but I am having difficulty imagining what this looks like as a picture. The only examples I've done thus far are ones where the wind was pointing either due north or at an angle smaller than $90^{\circ}$, and so I'm having trouble drawing a picture of the scenario - I'm not sure how the wind should displace the path of the airplane. Could somebody please draw me a picture? That's really all I need here to figure out the rest on my own. Thanks.

Consider the diagram below:

![airplane_velocity_in_wind_diagram](

The vector with length $130~\text{mph}$ at an angle of $45^\circ$ north of east represents the trajectory of the airplane in the absence of wind. The vector with magnitude $25~\text{mph}$ in the easterly direction represents the velocity of the wind. The vector $v$ represents the resultant velocity of the airplane.