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 the iron plate is 2 cm . A bullet fired goes through the wood first and then penetrates 1 cm into iron. A similar bullet fired with the same velocity from the opposite direction goes through iron first and then penetrates 2 cm into the wood. If a 1 and a 2 be the retardation offered to the bullet b

Step-by-step solution

Let a 1 and a 2 be the retardations offered to be bullet by wood and iron respectively. For A → B → C , v 1 2 - u 2 = 2 a 1 4 , and 0 2 - v 1 2 = 2 a 2 ( 1 ) Adding, we get - u 2 = 2 ( 4 a 1 + a 2 ) ...(i) For A ′ → B ′ → C ′ , v 2 2 - u 2 = 2 a 2 2 and 0 2 - v 2 2 = 2 a 1 2 Adding, we get - u 2 = 2 ( 2 a 1 + 2 a 2 ) ....(ii) Equating Eqs. (i) and (ii) and solving, we get 4 a 1 + a 2 = 2 a 1 + 2 a 2 ⇒ a 2 = 2 a 1