To take off from the ground, an airplane must reach a sufficiently high speed. T

Question

To take off from the ground, an airplane must reach a sufficiently high speed. The velocity required for the takeoff, the takeoff velocity, depends on several factors, including the weight of the aircraft and the wind velocity. A plane accelerates from rest at a constant rate of 5.00 m/s2 along a runway that is 1800 m long. Assume that the plane reaches the required takeoff velocity at the end of the runway. What is the time tTO needed to take off? What percentage of the takeoff velocity did the plane gain when it reached the midpoint of the runway?

Explanation / Answer

Vo = initial velocity = 0 m/s

a = acceleration = 5

d = distance travelled = 1800 m

t = time of travel

using the equation

d = Vo t + (0.5) a t2

1800 = 0 t + (0.5) (5) t2

t = 26.83 sec

d' = distance at midway = 900 m

V'f = final velocity at midway

Vf = final velocity at the end

using the equation

Vf = Vo + at

Vf = 0 + 5 (26.83)

Vf = 134.15 m/s

using the equation

V'f2 = Vo2 + 2 a d'

V'f2 = 02 + 2 (5) (900)

V'f = 94.86 m/s

%age = (94.86/134.15) x 100 = 70.7

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