# An empty airplane, whose mass is 120,000 [kg] has a take of acceleration of 2.0 [m/s2].?

a) What is the force acting on the plane?

b) What is the velocity of the plane at the end of a 1000 [ft] runway?

c) How long does it take for the plane to reach the end of the runway?

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a) What is the force acting on the plane?

a = acceleration = 2.0 m/s²

m = mass = 120,000 kg

F = force = to be determined

F = ma

F = (120,000 kg)(2.0 m/s²)

F = 240,000 N = 240 kN

b) What is the velocity of the plane at the end of a 1000 [ft] runway?

NOTE: I am going to assume that you actually mean a 1,000 m runway for two reasons:

(1) All of the other units in the problem are metric units rather than U.S. customary

units. (2) A 1,000 ft runway isn't really practical for any aircraft of the indicated mass.

Actually, a 1,000 m runway is too small for a 120,000 kg aircraft, as well.

Δx = runway length = 1,000 m

v0 = initial veocity = 0 m/s

a = acceleration = 2.0 m/s²

v = final velocity = to be determined

v² = (v0)² + 2aΔx

v² = (0 m/s)² + 2(2.0 m/s²)(1,000 m)

v² = 4,000 m²/s²

v = √( 4,000 m²/s²)

v = 63.2455532 m/s = 63.2 m/s

c) How long does it take for the plane to reach the end of the runway?

See the above NOTE.

v = v0 + at

v - v0 = at

(v - v0) / a = t

t = (v - v0) / a

t = (63.2 m/s - 0 m/s) / 2.0 m/s²

t = 31.6227766 s = 31.6 s

• a) What is the force F acting on the plane?

F = m*a = 1.2*10^5*2 = 2.4*10^5 N

b) What is the velocity V of the plane at the end of a L = 1000 [ft] runway?

V = √ 2*a*L = √ 2*2*1000*0.3048 = 35 m/sec (just two sign. digits)

c) How long t does it take for the plane to reach the end of the runway?

2d = V*t

t = 2d/V = 610/35 = 17 sec (just two sign. digits)