Question

The pilot of a small plane maintains an air speed of 66 knots (or nautical miles per hour) and wants to fly due North (0?) with respect to the Earth.

If a wind of 31 knots is blowing from the east (90?), calculate the heading (azimuth) the pilot must take.

Answer in units of ?.

020 (part 2 of 2) 5.0 points

What is the speed of the plane relative to the ground?

Answer in units of knots.

Got first part to be 28.015 degrees. Need help with second part

Answer 1

An aircraft flies relative to the air, not the ground. If the air is moving, the plane will be blown "off course" relative to the ground.
This wind is square on. That makes it simple.
The plane will still do its 66 kts in the northerly direction, but for every 66 kts. north, will be blown west 32 kts., without correction.
To compensate for that, the pilot must take a heading not north, but more east of north, in order to end up directly north.
So, the pilot turns the plane right to a heading of arctan (31/66) = 25.159 degrees east of north, or azimuth 030 will be close enough. That's where he/ she points the plane's nose to go.
The only problem with this is it takes longer to get to where he/ she intends. The aircraft speed over the ground will be sqrt. (66^2 - 31^2) = 58.26 kts in the north direction.