Question

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.

Answer 1

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