A rifle bullet loses 1/20th of its velocity in passing through a plank. find how many such uniform planks it would pass through before coming to rest assuming resistance to the plank to be uniform

# A rifle bullet loses 1/20th of its velocity in passing through a plank

If v is initial velocity of bullet, after loosing (1/20)th of initial velocity due to passing through wooden plank of depth d,

the velocity of the bullet becomes (19/20) v.

Retardation a created by wooden plank can be obtained from, " V^{2} = U^{2} - 2aS ", where V is final speed,

U is initial speed, S is the distance traveled and a is retardation.

hence we have, (19/20)^{2} v^{2} = v^{2} - (2×a×d ) or a = (39/400)v^{2}/ (2d) …(1)

if the final velocity of bullet is zero after passing through depth D, then we have, 0 = v^{2} - (2×a×D) …(2)

By substituting retardation a from eqn.(1) in eqn.(2), we get, v^{2} = [(39/400)v^{2}/ d ]×D or D/d = 400/39 ≈ 10

Hence 9 more planks of same depth d are required to stop the bullet