Question

An airplane flies at 120.0 m/s and banks at a 30° angle. If its mass is 2.50×10³ kg, (a) what is the magnitude of the lift force? (b) what is the radius of the turn?

a) 1.31 x 10⁴ N, 2.05 x 10³ m
b) 2.75 x 10⁴ N, 1.50 x 10³ m
c) 3.92 x 10⁴ N, 1.20 x 10³ m
d) 4.60 x 10⁴ N, 9.80 x 10² m

Answer 1

The magnitude of the lift force is 1.31 x 10⁴ N. The radius of the turn is 2.05 x 10³ m. Therefore, the correct answer is a) 1.31 x 10⁴ N, 2.05 x 10³ m.

Step-by-step explanation:

(a) To find the magnitude of the lift force, we can use the equation:

Lift force = (mass of the airplane) * (acceleration due to gravity) * (sin(angle of bank))

Substituting the given values:

Lift force = (2.50 x 10³ kg) * (9.80 m/s²) * (sin(30°))

Lift force = 1.31 x 10⁴ N

(b) To find the radius of the turn, we can use the equation:

radius = (velocity of the airplane)² / (acceleration due to gravity) * (tan(angle of bank))

Substituting the given values:

radius = (120.0 m/s)² / (9.80 m/s²) * (tan(30°))

radius = 2.05 x 10³ m