A target is made up of two plates, one wood and the other of iron. The thickness of the wooden plate is 4 cm and that of iron plate is 2 cm. A bullet fired goes through of the wood first and then penetrates 1 cm into iron. A similar bullet fired with same velocity from opposite direction goes through iron first and then penetrates 2 cm into wood. If a1 and a2 be the retardations offered to the bullet by wood and iron plates respectively, determine the relation between a1 and a2

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Let initial velocity of the bullet is u.for the first bullet fired in wood.change in kinetic energy=Work done by the forces0-12mu2=F1×x1 cos180+F2×x2 cos180-12mu2=-F1×x1 -F2×x2 12mu2=ma1×x1 +ma2×x2 12u2=a1×4 +a2×1u2=8a1+2a2...1for the second bullet fired in iron.0-12mu2=F3×x3 cos180+F4×x4 cos180-12mu2=-F3×x3 -F4×x4 12mu2=ma2×x3 +ma1×x4 12u2=a2×2+a2×2u2=4a1+4a2...2from eqn 1 and 28a1+2a2=4a1+4a24a1=2a2a1a2=24=12a2=2a1Regards

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