A bullet fired into a fixed target loses half its velocity after penetrating 3 cm . How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

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TestHub · Accepted Answer

For first part of penetration, by equation of motion,

$(\frac{u}{2})^{2} = (u)^{2} - 2 f (3)$

or $3 u^{2} = 24 f$

For latter part of penetration,

$0 = (\frac{u}{2})^{2} - 2 f x$

or $u^{2} = 8 f x$

Therefore,

$3 \times (8 f x) = 24 f$

or $x = 1 cm$

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