Questions
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
