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

Options

A. 22/3 cm
B. 40/3 cm
C. 20/3 cm
D. 22/5 cm

Answer

B

Explanation

For first part of penetration, by equation of motion
`(u/2)^(2) - (u)^(2) = 2aS` or `a = -(3u^(2))/(8S)` .. (i)
For later part of penetration
`(0)^(2) - (u/2)^(2) = 2aS^(')` or `S^(') = - u^(2)/8a`
`S^(') = u^(2)/8(8S)/(-3u^(2))` (Using (i))
`S^(') = S/3 = 40/3` cm (S = 40 cm given)