# Dynamics - Airplane stopping on a runway

auburntigers_dy

## Homework Statement

an airplane has a mass of 5Mg has a touchdown speed of 300m/hr. At which instant the braking parachute is deployed and the power shut off. If the total drag on the aircraft varies with velocity as shown in the accompanying graph, calculate the distance x along the runway required to reduce the speed to 150km/hr. Aproximate the variation of the drag by an equation D=k*(v^2). where 'k' is a constant.

## Homework Equations

integral of (vdv)=a* integrate ds

## The Attempt at a Solution

The constant 'k' was found to be 120,000 Newtons/(83m/s)^2
from the graph. Then, how to calculate the displacement is where the help is needed. The calculated answer from the back of the of the book is 201m. Any help on this problem would be appreciated.
thanks

## The Attempt at a Solution

#### Attachments

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Homework Helper
I see no "attempt at a solution". Are you not even trying?

Staff Emeritus
Gold Member
auburntigers_dy,

I don't think that the "relevant equation" you cited is all that relevant. Can you write down Newton's second law for this problem? That would be a good start.

auburntigers_dy
tom mattson,
Newton's second law is f=m*a. ma=kv^2. therefore a=(kv^2)/m. This is where the relevant equation that i cited could be used, where the acceleration is calculated and velocity is given which then leaves you with the unknown term delta x. I am stuck on what velocity would i use to solve for this delta x.

auburntigers_dy
dynamics

I see no "attempt at a solution". Are you not even trying?

Hallsofivy,

i solved for k, the drag force is kv^2 which i equated it to Newton's second law Mass*acceleration. Then solving for acceleration resulted in k*v^2/(5000kg). then I integrated the relevant the relevant equation vdv=ads to solve for ds. The confusion lies in the calculated acceleration which is also expressed in terms of velocity which leaves stuck upon how to solve for displacement.

auburntigers_dy
dynamics

I see no "attempt at a solution". Are you not even trying?

Hallsofivy,

i solved for k, the drag force is kv^2 which i equated it to Newton's second law Mass*acceleration. Then solving for acceleration resulted in k*v^2/(5000kg). then I integrated the relevant equation vdv=ads to solve for ds. The confusion lies in the calculated acceleration which is also expressed in terms of velocity which leaves me stuck upon how to solve for displacement. everything is expressed in terms of velocity.