You are designing an airport for small planes. One kind of airplane that might use this airfield must reach a speed before takeoff of at lea

Question

You are designing an airport for small planes. One kind of airplane that might use this airfield must reach a speed before takeoff of at least 27.8 m/s (100 km/h), and can accelerate at 2.00 m/s^2. a) If the runway is 150 meter long, can this airplane reach the required speed for takeoff? if not, what minimum length must the runway have?

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Delwyn 3 years 2021-08-11T05:34:26+00:00 1 Answers 65 views 0

Answers ( )

  1. Orla
    0
    2021-08-11T05:35:40+00:00
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    Explanation:

    Given that,

    Initial speed of the airfield, u = 0

    Final speed, v = 27.8 m/s

    Acceleration of the airfield, a=2\ m/s^2

    Length of the runway, d = 150 m

    Let v’ is the speed of the airplane to reach the required speed for takeoff. Finding v’ using third equation of motion as :

    v'^2-u^2=2ad\\\\v'=\sqrt{2ad} \\\\v'=\sqrt{2\times 2\times 150} \\\\v'=24.49\ m/s

    This speed is not enough as the airfield must reach a speed before takeoff of at least 27.8 m/s. Now, the required length of the runways is :

    v^2=2ax\\\\x=\dfrac{v^2}{2a}\\\\x=\dfrac{(27.8)^2}{2\times 2}\\\\x=193.21\ m

    So, the minimum length of the runways is 193.21 meters.

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