A Cessna airplane has a minimum take off speed of 28.3m/s. The length of the run

Question

A Cessna airplane has a minimum take off speed of 28.3m/s. The length of the runway is 600m. The plane takes off at an angle of 20 degrees from the horizon and continues to climb accelerate at 50% of the take-off acceleration for 41 minutes. The plane levels off and maintains its velocity for 52 minutes. The plane to experience minor mechanical issues and pilot decides to land at a small airport 2km away. The optimal landing speed is 21m/s. The maximum runway deceleration is 0.56 m/s^2. a) What is the minimum acceleration for take-off? b) What is cruising altitude during the flight? c) What is the cruising velocity? d) If the runway is 400m, can the plane land safely? e) What is the total horizontal displacement of the trip?

Explanation / Answer

a)

consider the motion along the horizontal direction

d = distance to be travelled = length of runway = 600 m

vo = initial velocity = 0 m/s

vf = final velocity = 28.3 m/s

a = acceleration

Using the equation

vf2 = vo2 + 2a d

28.32 = 02 + 2 (600)a

a = 0.67 m/s2

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