Projectile Motion Equations with Non-Constant Acceleration

[Nothing]

Hi

Does anyone know the projectile motion equations in which the acceleration is NOT constant?

 

[JasonRox]

Learn Calculus.

That's all you need.

 

[Nothing]

ahh...

Isn't there an equation(s) derived from the kinematic ones i can just apply?

 

[Integral]

There is no way that anybody can guess what you are asking for. You will have to ask an understandable question.

As for variable accelerations, just apply Newtons 3rd:

F=ma

 

[Creator]

Hi

Does anyone know the projectile motion equations in which the acceleration is NOT constant?
Isn't there an equation(s) derived from the kinematic ones i can just apply?

I believe you probably already know the standard proceedure here, Nothing.
Usually, beginning with F = ma,
just take the derivative of both sides of the equation since you are looking for the time rate of change of accel.

dF/dt = m(dA/dt)

However, the effectiveness of this equation goes beyond the original assumptions in Newton's law. In cases of rapid change of acceleration a modification of Newton's law is probable.

Is that what you are getting at?

Creator

 

[da_willem]

F=ma is a differential equation since a =d^2 x /dt^2 with x, a and F vectors. Given a certain force you can find the velocity or position as a function of time by integrating the force respectively one or two times. But you indeed need to know some calculus for that...

 

[Alkatran]

Is the change in acceleration constant?

Doesnt:
Position = Sum(x(i)*t^i/i!)

where i goes from 0 to infinity, x(0) is initial position, x(1) is inital speed, x(2) is inital acceleration, etc...

 

[Nothing]

ok u know that equation:

y = v0 sin (theta) - 0.5at^2 ?

where v0 sin (theta) is the vertical component the muzzle velocity

is there a counterpart where a is not constant?

 

[arildno]

Sure, you have:
y(t)=v_{0}t\sin\theta-\int_{0}^{t}(\int_{0}^{\tau}a(s)ds)d\tau

 

[Nothing]

thanks arildno, that really helped.