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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 
Asked by Sunita | 06 Jun, 2019, 23:37: PM
answered-by-expert Expert Answer
If v is initial velocity of bullet, after loosing (1/20)th of initial velocity due to passing through wooden plank of depth d,
velocity of bullet becomes (19/20)v .
 
Retardation a created by wooden plank can be obtained from,   " V2 = U2 - 2aS ", where V is final speed,
U is initial speed, S is the ditance travelled and a is retardation.
 
hence we have,   (19/20)2 v2 = v2 - (2×a×d )    or  a = (39/400)v2/ (2d)  ..........................(1)
 
if final velocity of bullet is zero after passing through depth D,  then we have,  0 = v2 - (2×a×D) ..........................(2)
 
By substituting retardation a from eqn.(1) in eqn.(2), we get,  v2 = [(39/400)v2/ d ]×D    or  D/d = 400/39 ≈ 10
 
Hence 9 more planks of same depth d is required to stop the bullet
Answered by Thiyagarajan K | 07 Jun, 2019, 09:38: AM

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