A bullet starts with some initial velocity .
It hits a plank which reduces it's velocity by .
Let be the number of planks required to stop it.
So on further calculations, I knew that
Is it correct? I am unsure as
Then approx .
This means that the larger the velocity the plank will decrease, the larger will be the no. of planks required. This is quite weird as it should be the opposite.
Now, this is how I got my formula.
Note: All symbols have their usual meaning like and .
Let the no. of planks required be
Let a plank decrease it's velocity by
Let thickness of one plank be
After crossing the first plank ,
Now, by third equation of motion for the first plank,
Now after crossing planks, it's velocity will be 0.
Now by again applying third equation of motion we get,
I hope that this is correct.