Hi I'm new to vectors and I really do not understand how one part came about.
An airplane needs to fly due east from one city to another at a speed of 400 kmh¡1. However, a 50 kmh¡1 wind blows constantly from the north-east.
In what direction must the aeroplane head to compensate for the wind, and how does the wind affect its speed?
Adapted from: IB HL Mathematics Haese and Harris Publications.
I understand everything about the question like the vector part and all I am just wondering how to get the angle. To calculate the speed the airplane should travel at so as to not be disrupted by the wind vector, the textbook says to use the cosine rule to find out. I understand why but when substituting the values into the cosine rule equation, there is a 135 degrees, which corresponds to the vector which the airplane should ideally travel at to avoid the wind. How did the 135 degrees come about? Can someone help me? Where in the question can I deduce 135 degrees and if there are any steps, could you please list them out? I really need to understand this to continue doing the other questions..
Thank you so so so much.