10 planks are required to stop the bullet in initial velocity u thickness of each planks is x and all planks are producing equal retardation find the final velocity of bullet after coming out of first plank
I am not certain what you mean by "equal retardation". Is that equal force, or equally absorbing energy?
Assuming equal force..
force*timeinPlank=mass*changeinvelocity
force=mass*changeV/time=mass*acceleration
so if each force is the same, acceleration is constant.
vf^2=vi^2+2ad
now on ten planks
0=u^2+2a*thickness*10
where thickness is the thickness of one plank.
so a=u^2/20t
on the first plank
vf^2=u^2+2a*thickness
vf^2=u^2+2u^2/20thick *thickness
vf^2=u^2(1-1/10)=9/10 u^2
vf=u sqrt(9/10)