Question

An airplane of mass 1.6 ? 10⁴ kg is moving at 62 m/s. The pilot then revs up the engine so that the forward thrust by the air around the propeller becomes 7.4 ? 10⁴ N. If the force exerted by air resistance on the body of the airplane has a magnitude of 6.0 ? 10⁴ N, find the speed of the airplane after it has traveled 500 m. Assume that the airplane is in level flight throughout this motion.
_____ m/s

Answer 1

Mass of the airplane = m = 1.6 x 10⁴ kg

Thrust force of the engine = F₁ = 7.4 x 10⁴ N

Air resistance on the airplane = F₂ = 6 x 10⁴ N

Acceleration of the airplane = a

ma = F₁ - F₂

(1.6x10⁴)a = 7.4x10⁴ - 6x10⁴

a = 0.875 m/s²

Initial speed of the airplane = V₁ = 62 m/s

Final speed of the airplane = V₂

Distance traveled by the airplane = D = 500 m

V₂² = V₁² + 2aD

V₂² = (62)² + (2)(0.875)(500)

V₂ = 68.5 m/s

Speed of the airplane after it has traveled 500 m = 68.5 m/s