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Question

A target is made of two plates,one of 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 the wood first and then penetrates 1 cm into iron. A similar bullet 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 then.

(a) a1 = 2a2

(b) a2= 2a1

(c) a1 = a2

(d) Data insufficient

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Solution

Dear student

Let the velocity with which bullet enters the woodenn plank be u and velocity at the interface of iron and wooden plank be v.considering motion in the wooden plank v2-u2=-2a×(4)v2=u2-8a1considering motion in the iron plank 02-v2=-2a2×(1)0=v2-2a20=u2-8a1-2a2u2=8a1+2a2...Aconsidering motion in the iron plank firstv12-u2=-2a2×(2)v12=u2-4a2considering motion in the wooden plank 02-v12=-2a1×(2)v12=4a1u2-4a2=4a1u2=4a2+4a1...Bfrom eqn A and B8a1+2a2=4a2+4a14a1=2a2a2=2a1Regards

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