What airspeed would a plane have to travel to have a groundspeed of 320 km/h [S] if there is a 50.0 km/h wind coming from the northwest?
To find the airspeed of the plane needed to maintain a groundspeed of 320 km/h in the presence of a crosswind, we will use the concept of vector addition.
Groundspeed is the resultant vector of the combination of airspeed and wind speed. Since the wind is coming from the northwest, it forms a right angle with the direction of the plane's travel. This results in a right triangle formed by the groundspeed vector, airspeed vector, and wind vector.
We can use the Pythagorean theorem to solve for the airspeed:
Groundspeed^2 = Airspeed^2 + Wind speed^2
In this case:
Groundspeed = 320 km/h
Wind speed = 50 km/h
Let's substitute the values into the equation:
320^2 = Airspeed^2 + 50^2
102,400 = Airspeed^2 + 2,500
Airspeed^2 = 102,400 - 2,500
Airspeed^2 = 99,900
To solve for the airspeed, we take the square root of both sides:
Airspeed = √99,900
Airspeed ≈ 316.18 km/h
Therefore, the plane would have to travel at an airspeed of approximately 316.18 km/h to maintain a groundspeed of 320 km/h with a 50.0 km/h wind coming from the northwest.
airspeed: use the law of cosines
s^2=320^2+50^2-2*320*50*cos45