A bullet fired into a wooden block loses half of its velocity after penetrating 40 cm. It comes to rest after penetrating a further distance of

Question

Smart Achievers · Accepted Answer

(2)

For first part of penetration, by equation of motion

${(\frac{u}{2})}^{2} - {(u)}^{2} = 2 a S$ or $a = \frac{- 3 u^{2}}{8 S}$ $. . . (i)$

For later part of penetration,

${(0)}^{2} - {(\frac{u}{2})}^{2} = 2 a S'$ or $S' = \frac{- u^{2}}{8 a}$

$S' = \frac{- u^{2}}{8} (\frac{8 S}{- 3 u^{2}})$ (Using (i)),

$S' = \frac{S}{3} = \frac{40}{3} cm$ $(∵ S = 40 cm given)$

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