1) A plane takes off from an O'Hare runway heading due west with a speed of 210.1 m/s. Once in the air, it encounters a north wind (blowing south) with a speed of 55.0 m/s. What is the magnitude of its velocity relative to the ground? 2) What is the direction of the resulting velocity (relative to its initial direction)?

I found this online Idek if it helps but First, determine how many degrees off the runway heading the reported wind is. So if you’re landing Runway 18 and the wind is 160 at 10, the wind is 20 degrees off the runway (180-160=20) . Now picture an analog clock face. How far is the wind angle number in minutes around the clock face? A wind angle of 20 degrees means 20 minutes around the clock face, which is one-third of the way around the clock face The crosswind component is one-third of the total wind. In this example, 10 knots * 1/3 = 3.3 knots of crosswind.

If you like charts, you can lay out common numbers and interpolate between them:

10-degree wind angle10 minutes, which is 1/6 around clockfacecrosswind = 1/6 * total wind
15-degree wind angle15 minutes, which is 1/4 around clockfacecrosswind = 1/4 * total wind
20-degree wind angle20 minutes, which is 1/3 around clockfacecrosswind = 1/3 * total wind
30-degree wind angle30 minutes, which is 1/2 around clockfacecrosswind = 1/2 * total wind
45-degree wind angle45 minutes, which is 3/4 around clockfacecrosswind = 3/4 * total wind
60-degree wind angle or more60 minutes, which is 100 percent of the way around a clockfacecrosswind component ≈ total wind speed