airplane has a steady thrust force of 10,000 N in the forward direction and has a constant velocity of 200 m/s. It then has an upgraded engi?

Question

An airplane has a steady thrust force of 10,000 N in the forward direction and has a constant velocity of 200 m/s. It then has an upgraded engine and thrusts 40,000 N. How fast is its velocity. Do not ignore air resistance.
Options for answers:
A) 200 m/s
B) 280 m/s
C) 400 m/s
D) 3200 m/s

Answer 1

At constant velocity:

Thrust = Drag



Drag is proportional to the square of velocity:

D = k v²



Substituting:

10,000 N = k (200 m/s)²

k = 0.25 kg/m



After the upgrade:

40,000 N = (0.25 kg/m) v²

v² = 160,000 m²/s²

v = 400 m/s



C.

Answer 2

40,000/10,000 = 4



√4 = 2



200m/s * 2 = 400m/s

Answer 3

Since, at constant velocity: Thrust = Drag

and

Drag is proportional to the square of velocity: D = k v²

So,

10,000 N = k (200 m/s)² ==> k = 0.25 kg/m,

Now,

40,000 N = (0.25 kg/m) v² , ==> v² = 160,000 m²/s²

Or,

v = 400 m/s . <--------------------------------/