Aim: To establish a physical model that calculates the velocity of raindrop

In the previous project, we analyzed the “parachutist falling” problem, where the air resistance is modeled as linearly or squarely proportional to velocity.

Yet, we must realize that the situlation is more complex for a pratical problem. Taking the droping of raindrop as an example, the resistance is not simply propotional to velocity, but is also relevant to the drop’s mass (or size).

Moreover, the shape of the raindrop is also changing with velocity, which may also affect the droping speed in turn.

In this project, I tried to establish a physical model to calcuate the velocity of raindrop by reviewing literatures.

Then, using Newton’s law, we calculated df/dt.

There were 2 ways to derive the equation which are Analytical method and numerical method.

One difference is that analytical method comes with exact solution and numerical solution comes with approximate solution.

However, there are some cases where it is really hard to derive certain equation which will take a lot of time.

In this case we use analytical method, thhe thing that differs from the falling parachutist is that there are several qualities that we must care about since it is a practical problem.