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29 January, 08:48

Airplane A, starting from rest with constant acceleration, requires a runway 400 m long to become airborne. Airplane B requires a takeoff speed twice as great as that of airplane A, but has the same acceleration, and both planes start from rest.

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  1. 29 January, 09:11
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    1. How long must the runway be for airplane B

    2. If airplane A takes time T to travel the length of its runway, how long (in terms of T) will airplane B take to travel the length of its runway?

    Explanation:

    Constant acceleration question

    Airplane A start from rest

    Then, the initial velocity is u=0m/s.

    The runaway before is flight is 400m.

    Time A use to travel is T

    Therefore, t1=T

    For plane B

    Airplane B starts from rest too

    i. e u=0m/s.

    Let the distance Plane B covers be L.

    Let the time plane B use to travel be t

    Given that they both have the same acceleration

    Then,

    The final speed of airplane B is twice that of plane A.

    Let the final speed of plane A = x

    Then, final speed of plane B = 2x.

    Using equation of motion

    V=u+at

    V^2=U^2+2as

    S=ut+1/2at^2

    For plane A

    V=u+at; x=0+aT,

    since T is time plane A use to travel

    x=aT

    For plane B

    V=u+at; 2x=0+at

    Since t is the time plane B use

    2x=at Equation 2

    Then, substituting x into equation 2

    2 (aT) = at

    Then

    2aT=at.

    Divide both side by a, since the both have the same acceleration

    2T=t

    Also using

    V^2=U^2+2as

    Plane A.

    (x) ^2=0^2+2 (a) (400)

    x^2=800a

    Plane B

    (2x) ^2=0^2+2 (a) (L)

    4x^2=2aL

    divide both side by 2

    2x^2=aL

    Now substituting x^2=800a

    2 (800a) = aL

    1600a=aL

    Since they both have the same acceleration, divide both side by a

    Then,

    L=1600m

    1. The runway distance the plane B will cover is 1600m

    2. And the time B will cover the runway in terms of time (T) A covers is run way.

    t=2T

    i. e twice the time plane A will cover it owns distance
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