Question

I am working on writing a differential equation for velocity can someone give me assistance. i am doing it based on the speed a specific ball is kicked. How should I start.

Answer 1

Find out all the forces on the ball at the moment of impact and during flight

This includes force of gravity (in horizontal direction)

The impact (kick/throw)

Air resistance during flight (typically depends on the material use and can be ignored if ball size is small)

So one sample differential equation can be where m is mass of ball and k is the drag coefficient

That gives which is a second order equation

Initial conditions would be with being the initial velocity with which it is thrown

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