A bullet is fired into a fixed target looses one third of its velocity after travelling 4cm. It penetrates further m before coming to rest. The value of D is

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Solution

Q.
A bullet is fired into a fixed target looses one third of its velocity after travelling 4cm. It penetrates further $D \times 10^{- 3}$ m before coming to rest. The value of D is [2024]

1 32

2 5

3 3

4 4

Ans.
(1)

    $v^{2} - u^{2} = 2 a s$

${(\frac{2 u}{3})}^{2} = u^{2} + 2 (- a) (4 \times 10^{- 2})$

   $\frac{4 u^{2}}{9} = u^{2} - 2 a (4 \times 10^{- 2})$

   $- \frac{5 u^{2}}{9} = - 2 a (4 \times 10^{- 2})$ ...(1)

$0 = {(\frac{2 u}{3})}^{2} + 2 (- a) (x)$

$- \frac{4 u^{2}}{9} = - 2 a x$ ...(2)

$(1) / (2), \frac{5}{4} = \frac{4 \times 10^{- 2}}{x}$

   $x = \frac{16}{5} \times 10^{- 2}$

   $x = 3.2 \times 10^{- 2} m$

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