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Suppose we have a free falling object inside a planet's gravitational field with strength g.The planet's atmosphere provides a drag force which is dependant from the u^2 of the particle. Suppose t...
#2: Post edited
by
MissMulan
·
2022-08-20T17:22:17Z (over 1 year ago)
- Suppose we have a free falling object inside a planet's gravitational field with strength g.The planet's atmosphere provides a drag force which is dependant from the u^2 of the particle.
- Suppose the weight of the object is m1g and the drag force due to the atmosphere is -ku^2 and lets say we set k=1 for simplicity we end up with this differential equation:
- $$\frac{du}{dt} = g+\frac{u^{2}}{m_{1}} $$
- and if you solve the differential equation with initial condition u(0)=0 you get
$$u(t) =\sqrt{g}\cdot \sqrt{m_{1}} \cdot tan(\sqrt{g}\sqrt{m_{1}}t) $$- If I graph the function in Desmos it shows me [this](https://www.desmos.com/calculator/gvusyqx0ab)
- However we have infinities involved and I dont think it is right.What am I missing?
- Suppose we have a free falling object inside a planet's gravitational field with strength g.The planet's atmosphere provides a drag force which is dependant from the u^2 of the particle.
- Suppose the weight of the object is m1g and the drag force due to the atmosphere is -ku^2 and lets say we set k=1 for simplicity we end up with this differential equation:
- $$\frac{du}{dt} = g+\frac{u^{2}}{m_{1}} $$
- and if you solve the differential equation with initial condition u(0)=0 you get
- $$u(t) =\frac{\sqrt{g}}{\sqrt{m_{1}}}\cdot tan(\sqrt{g}\sqrt{m_{1}}t) $$
- If I graph the function in Desmos it shows me [this](https://www.desmos.com/calculator/gvusyqx0ab)
- However we have infinities involved and I dont think it is right.What am I missing?
#1: Initial revision
by
MissMulan
·
2022-08-20T16:39:20Z (over 1 year ago)
Differential equation solution cannot describe what happens in reality
Suppose we have a free falling object inside a planet's gravitational field with strength g.The planet's atmosphere provides a drag force which is dependant from the u^2 of the particle.
Suppose the weight of the object is m1g and the drag force due to the atmosphere is -ku^2 and lets say we set k=1 for simplicity we end up with this differential equation:
$$\frac{du}{dt} = g+\frac{u^{2}}{m_{1}} $$
and if you solve the differential equation with initial condition u(0)=0 you get
$$u(t) =\sqrt{g}\cdot \sqrt{m_{1}} \cdot tan(\sqrt{g}\sqrt{m_{1}}t) $$
If I graph the function in Desmos it shows me [this](https://www.desmos.com/calculator/gvusyqx0ab)
However we have infinities involved and I dont think it is right.What am I missing?