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. W

Question

3 years ago

5

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. W

hat is the plane's actual speed and direction? Round angles to the nearest degree and other values to the nearest tenth.

Mathematics

1 answer:

kogti [31] · Answer 1 · 2022-05-08T00:37:27+03:00

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

calculate the resultant force R
F1x=150 F1y=0 F2x= 0 F2y=30
Rx=F1x+F2x------------- >150+0 ---------------- >Rx=150
</span>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)