A bulled fired into a fixed wooden block loses half of its velocity after penetrating 40cm. 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

Let initial velocity of body at point A is v, AB is 40 cm

From `v^2=u^2-2as`
`implies (v/2)^2=v^2-2a times 40`
or `a=(3v^2)/320`
Let on penetrating 40cm in a wooden block, the body moves x distance from B to C.
So, for B to C
`u=V/2,v=0`
`s=x, a=(3v^2)/320` (deceleration)
`therefore (0)^2=(v/2)^2-2 times (3v^2)/320 times x`
or `x=40/3cm`