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. `6.66 cm`
B. `3.33 cm`
C. `12.5 cm`
D. 10 cm

Answer

A

Explanation

Given, Initial velocity, U =v
Final velocity, `V = (v)/(2)`
Distance , `s = 20 cm`
Let, the further distance of penetration before it comes to rest be x.
`V ^(2) = U ^(2) - 2as`
`((V)/(2)) ^(2) = v ^(2) - 2a xx 20`
`40a = v ^(2) - ( v ^(2))/(4)`
`40 a = ( 3v ^(2))/( 4) " "...(i)`
and `v ^(2) = u ^(2) + 2 as`
`v ^(2) = 0 + 2a xx (2 0 +x )`
`v ^(2) = 2 xx (3)/(160) v ^(2) xx (20 + x)`
[From Eq. (i)]
`1 = (3)/(80) (20 + x)`
`(80)/(3) = 20 + x `
`x = (80)/(3) - 20`
`x = (80-60)/(3)`
`x = (20)/(3) = 6.66 cm`