a bullet fired on to a wooden plank.in penetrating trough the plank it lose 10% of its kinetic energy. how many planks are required just to stop the bullet?

as from the wuation. it says bullet loses (10)^-1/2 of velocity upon penetration into each plank

I feel that this data is not enough. A lot more data is required like

we need to know the minimum velocity required to pass through a single plank.??

how far away are you shooting?
how thick are the planks?
how far apart are the planks?

definitely not enough info to answer. but technically the least that COULD stop it if the variables are right is 2 or 3.

Let thickness of one plank be = d.

KE1 = 0.5*m*v²

KE2 = 0.5*m*v ₂²  = 0.9 *0.5*m*v²    So,   v ₂²  = 0.9 *v²   .

Let us calculate deceleration produced by one plank using  v ₂²  = v ₁²  -  2*a*d

So,   2*a =  (0.1*v²) / (d).

Final velocity  =  0 m/s.

So, 0 = v ²  -  2*a*d₁ 

d₁ =  v ² / (2*a)  = v ² / ((0.1*v²) / (d)) = 10*d.

So, 

d₁ =   10*d.

Since one Plank is of thickness d,  10*d is thickness of 10 planks.

So,   10 planks are required just to stop the bullet.