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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, 11:37: PM
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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