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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1.0 cm

1.5 cm

2.0 cm

3.0 cm

answer is A.

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Detailed Solution

see fig

Hero we have

${(\frac{v}{2})}^{2} = v^{2} - 2 a \times 3 Solving, we get a = v^{2} / 8 When the bullet comes to rest, we have 0 = {(\frac{v}{2})}^{2} - 2 \times \frac{v^{2}}{8} \times x or \frac{v^{2}}{4} = \frac{v^{2}}{4} \times x or x = 1 cm$

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