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Vertical trajectory of a projectile with quadratic drag

(Elaborating on @LPZ's [solution 283846]) If you solve for arbitrary constant of drag $d$, and gravitational acceleration $a$, using $$\dot v=-a-d\ \text{sgn}(v)\,v^2$$ this leads to a concise ...
Jos Bergervoet's user avatar
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Trajectories of projectile based on different speeds of projection

According to classical dynamics (Marion and Thornton, Central Force motion chapter), the eccentricity $\epsilon$ of the trajectory of two bodies in central motion is given by: $\epsilon = \sqrt{1 + \...
cconsta1's user avatar
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Vertical trajectory of a projectile with quadratic drag

Yes, if your trajectory is vertical, there is a simple analytic solution for a purely quadratic drag. In dimensionless units (unit mass, terminal velocity speed unit), you need to solve: $$ \dot v + v^...
LPZ's user avatar
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Time of a ball going up and down with air resistance

In addition to the gravitational force, we now have the drag force. On the way up, both these forces act downward. So the ball experiences an increased net acceleration. This implies that the ...
Fatima Qurat ul Ain's user avatar
16 votes
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Why does the cross section of a metal after a hypervelocity impact look like that?

I believe that this is a form of spallation. The impact causes a stress wave which travels through the material. These waves reflect off the back and sides of the plate, leading to a region of even ...
Riley Scott Jacob's user avatar
1 vote

What happens to $\frac{d}{dt}\left(\hat{v}\right)$ at the highest point a projectile reaches when launched vertically upwards?

This is a fun question, you can answer your own question by looking at a simple example. Let's look at vertical motion under the influence of gravity: $$v(t)=v_0-gt\rightarrow v(t)=-gt$$ Where $g>0$...
QPhysl's user avatar
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1 vote

General solution for the motion of a 1D particle with drag

For what it is worth, any autonomous 1D 2nd-order ODE $\ddot{x}=a(x,\dot{x})$ can be written as an autonomous 2D 1st-order ODE $$\begin{align}\dot{x}~=~&v,\cr \dot{v}~=~&a(x,v),\end{align}$$ ...
Qmechanic's user avatar
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8 votes
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Need help regarding projectile motion

A projectile is typically defined as an object given some initial impulse, which travels through space under only the force of gravity and possibly drag or thrust. Once an object hits the ground, it's ...
Nuclear Hoagie's user avatar
2 votes

Need help regarding projectile motion

With an angle of zero degrees, I assume that you mean that you are dealing with horizontal motion - that being motion only along the $x$ axis - with no vertical movement up or down. Maybe this is a ...
Steeven's user avatar
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