Hello welcome to Eroniana...how are you guys? i hope you are always fine. Before i start discuss about this post i want to say thank you for all of you for taking your time to read this post.

In this post i will share with you how to get polynomial equation from the plane height associated with landing distance and looking for the plane acceleration in y direction if the velocity in x direction is always constant.

First let's review the problem we face and get the boundary condition related with this situation

The initial condition described is when the x is zero then the velocity of y direction at h is equal to zero, and when x is equal to L the velocity of y direction also zero

Now we have obtain four boundary condition, that's it initial and final condition of plane position and velocity

With using polinomyal approch we can find the ideal equation of plane height related with landing distance.

After we get the boundary condition, now we must subtitute all equation we get and find the form of a, b, c, and d related with it's height and landing distance.

Ok after we bet the form of a, b, c, and d the next step is subtitute the form of a,b,c,d to the polynom equation that we assume before, and after that we get the equation P(x) = y = equation of height related with landing distance

For the second cases, if we want to get the form of acceleration equation, the simple way to get it is just derrive the y equation twice depend on time

We assume the velocity in x direction always constant dx/dt = v = constant

So we get the accelerate equation in y direction...

ok i think that's all can i share to you maybe it's not perfect and maybe there is some mistake in my grammar and the way i'm using english...but i hope this post can help you to understand much about calculus and thank you for read my post...you can write your opinion in comment below to make this blog more efficient and better every single day... :)

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