# 1D Kinematics problem with a plane taking off

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1. Jul 5, 2017

### Granger

1. The problem statement, all variables and given/known data
An Airbus 380 needs to reach the velocity of 280 kmh^-1 before it takes off. The maximum acceleration the plain reaches in the runway is 0.95 ms^-2. Verify THAT the plane can use an airport with this runways.
Runway 1: 3805 meters (SSW-NNE)
Runway 2: 2400 meters (S-N)

2. Relevant equations
$$x=x_0+v_0 t + 1/2 a t^2$$
$$v= v_0 + at$$

3. The attempt at a solution
At first I thought this was a pretty easy problem.
Using equations of motion:
$$x=1/2 a t^2$$
$$v= at$$

For the first runway, solving
$$3805=1/2 \times 0.95 \times t^2$$
$$t=89.5 s$$

$$v= 0.95 \times 89.5$$
$$v=85.05 ms^-1$$

Which confirms it can use this runway (since the velocity is bigger than the necessary velocity).

However for the second runway, I get

$$2400=1/2 \times 0.95 \times t^2$$
$$t=71.1 s$$

$$v= 0.95 \times 71.1$$
$$v=67.545 ms^-1$$

Which is inferior to the necessary velocity. But that contradicts the problem statement that it can indeed use the airport.

I might be making an incorrect assumption. I suspect it might be related to the acceleration. In fact they say that's the maximum acceleration not the acceleration. So the might be a time dependence on the acceleration?
But how do I determine it?

Thanks!

2. Jul 5, 2017

### Staff: Mentor

Does a plane have to be able to use every runway at an airport in order for it to use that airport? The problem statement doesn't give any direct guidance on this matter, so I think that you are free to impose your own (reasonable) assumption. Just state up front in your answer what assumption you choose.