Answer:
1371.26 Km
Explanation:
First of all, we need to find the velocity of the plane relative to the ground since the air has a velocity of 78.2 m/s due east and without any wind, it flies at a velocity of 188 m/s.
Thus, during the west trip, the velocity will be;
Vw = Vp - Va
Vp is velocity of plane while Va is velocity of air
and since distance/time = velocity ;
Time = velocity/distance and thus;
Time during this west period ;Tw = X/(Vp - Va)
Now during the east trip,
Ve = Vp + Va
And Te = X/(Vp + Va)
From the question, the plane can fly 4.9 hours on a full load of fuel. Let's convert this to seconds because velocity is in m/s
Thus, 4.9 hours = 4.9 x 60 x 60 = 17640 seconds
So, this time will be equal to the sum of that in the west and east directions.
Thus; T = Tw + Te
From above we know Tw and Te.
Let's substitute them into the equation;
T = [X/(Vp - Va)] + [X/(Vp + Va)]
T = X[(Vp + Va + Vp - Va)/((Vp)² — (Va)²)
T = X[(2Vp)/((Vp)² — (Va)²)
Making X the subject to obtain;
X = [T((Vp)² — (Va)²)]/(2Vp)
X = [17640((188)² — (78.2)²)]/(2 x 188)
X = 515595326.4/376 = 1371264.17m = 1371.26 Km
