Question

A single-engine airplane is heading due east at a constant speed of 150 mi / h. There is a 30 mi / h cross wind blowing north. What is the plane's actual speed and direction? Round angles to the nearest degree and other values to the nearest tenth.

Answer 1

Let
F1------------------------- > airplane speed 150 mi / h East
F2-------------------------- > wind  speed 30 mi / h North

calculate the resultant force R
F1x=150    F1y=0      F2x= 0  F2y=30
Rx=F1x+F2x------------- >150+0 ---------------- >Rx=150
Ry=F1y+F2y------------- >0+30 ---------------- >Rx=30
║R║=√150² 30²=√23400=152.97----- >153 mi/h
tan(theta)=Ry/Rx=30/150=0.20
arctan (0.20)=11.31 degrees-----------11.3 degrees

 the answer is
actual speed 153 mi/h and direction 11.3 degrees North-East  (I Quadrant)