Q. A target is made of two plates, one of wood and the other of iron. The thickness of the wooden plate is and that of the iron plate is . A bullet fired goes through the wood first and then penetrates into iron. A similar bullet fired with the same velocity from the opposite direction goes through iron first and then penetrates into the wood. If and be the retardation offered to the bullet by wood and iron plates respectively, then

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Solution:

Let and be the retardations offered to be bullet by wood and iron respectively.
For
and
Adding, we get
...(i)
For

and
Adding, we get
....(ii)
Equating Eqs. (i) and (ii) and solving, we get